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Formal algebraic geometry Summary Formal_scheme A locally Noetherian scheme is a locally Noetherian formal scheme in the canonical way: the formal completion along itself. In other words, the category of locally Noetherian formal schemes contains all locally Noetherian schemes. Formal schemes were motivated by and gene... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck-Riemann-Roch theorem Summary Grothendieck-Riemann-Roch_theorem In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds, which is itself a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck-Riemann-Roch theorem Summary Grothendieck-Riemann-Roch_theorem The Grothendieck–Riemann–Roch theorem sets both theorems in a relative situation of a morphism between two manifolds (or more general schemes) and changes the theorem from a statement about a single bundle, to one applying to chain complexes of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck-Riemann-Roch theorem Summary Grothendieck-Riemann-Roch_theorem Conversely, complex analytic analogues of the Grothendieck–Riemann–Roch theorem can be proved using the index theorem for families. Alexander Grothendieck gave a first proof in a 1957 manuscript, later published. Armand Borel and Jean-Pierre Se... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fiber product of schemes Summary Base_change_(scheme_theory) In mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction. It has many interpretations and special cases. For example, the fiber product describes how an algebraic variety over one field determines a variet... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Inverse image functor Summary Inverse_image_sheaf In mathematics, specifically in algebraic topology and algebraic geometry, an inverse image functor is a contravariant construction of sheaves; here “contravariant” in the sense given a map f: X → Y {\displaystyle f:X\to Y} , the inverse image functor is a functor from ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dimension axiom Summary Eilenberg–Steenrod_axioms In mathematics, specifically in algebraic topology, the Eilenberg–Steenrod axioms are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular homology, developed by Samuel ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eilenberg–Zilber theorem Summary Eilenberg–Zilber_theorem In mathematics, specifically in algebraic topology, the Eilenberg–Zilber theorem is an important result in establishing the link between the homology groups of a product space X × Y {\displaystyle X\times Y} and those of the spaces X {\displaystyle X} and Y {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euler class Summary Euler_class In mathematics, specifically in algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth manifold, it generalizes the cl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cup product Summary Cup_product In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an associative (and distributive) graded commutative product operation in cohomology, turning the cohomolo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hartogs number Summary Hartogs_number In mathematics, specifically in axiomatic set theory, a Hartogs number is an ordinal number associated with a set. In particular, if X is any set, then the Hartogs number of X is the least ordinal α such that there is no injection from α into X. If X can be well-ordered then the ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithmic differential Summary Logarithmic_derivative In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where f ′ {\displaystyle f'} is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stabilization hypothesis Summary Stabilization_hypothesis In mathematics, specifically in category theory and algebraic topology, the Baez–Dolan stabilization hypothesis, proposed in (Baez & Dolan 1995), states that suspension of a weak n-category has no more essential effect after n + 2 times. Precisely, it states tha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Day convolution Summary Day_convolution In mathematics, specifically in category theory, Day convolution is an operation on functors that can be seen as a categorified version of function convolution. It was first introduced by Brian Day in 1970 in the general context of enriched functor categories. Day convolution act... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
F-algebra Summary F-algebra In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a sin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Essentially surjective functor Summary Essentially_surjective_functor In mathematics, specifically in category theory, a functor F: C → D {\displaystyle F:C\to D} is essentially surjective (or dense) if each object d {\displaystyle d} of D {\displaystyle D} is isomorphic to an object of the form F c {\displaystyle Fc} ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Preabelian category Summary Preabelian_category In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more detail, this means that a category C is pre-abelian if: C is preadditive, that is enriched over the monoidal category of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Preadditive categories Summary Pre-additive_category In mathematics, specifically in category theory, a preadditive category is another name for an Ab-category, i.e., a category that is enriched over the category of abelian groups, Ab. That is, an Ab-category C is a category such that every hom-set Hom(A,B) in C has th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pseudo-abelian category Summary Pseudo-abelian_category In mathematics, specifically in category theory, a pseudo-abelian category is a category that is preadditive and is such that every idempotent has a kernel. Recall that an idempotent morphism p {\displaystyle p} is an endomorphism of an object with the property th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quasi-abelian category Summary Quasi-abelian_category In mathematics, specifically in category theory, a quasi-abelian category is a pre-abelian category in which the pushout of a kernel along arbitrary morphisms is again a kernel and, dually, the pullback of a cokernel along arbitrary morphisms is again a cokernel. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Semi-abelian category Summary Semi-abelian_category In mathematics, specifically in category theory, a semi-abelian category is a pre-abelian category in which the induced morphism f ¯: coim f → im f {\displaystyle {\overline {f}}:\operatorname {coim} f\rightarrow \operatorname {im} f} is a bimorphism, i.e., a mono... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
F-coalgebra Summary F-coalgebra In mathematics, specifically in category theory, an F {\displaystyle F} -coalgebra is a structure defined according to a functor F {\displaystyle F} , with specific properties as defined below. For both algebras and coalgebras, a functor is a convenient and general way of organizing a si... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Additive category Summary Additive_category In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exponential object Summary Exponential_object In mathematics, specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed categories. Categories (such as ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extranatural transformation Summary Extranatural_transformation In mathematics, specifically in category theory, an extranatural transformation is a generalization of the notion of natural transformation. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Canonical bifunctor Summary Internal_Hom_functor In mathematics, specifically in category theory, hom-sets (i.e. sets of morphisms between objects) give rise to important functors to the category of sets. These functors are called hom-functors and have numerous applications in category theory and other branches of math... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of small categories Summary Category_of_small_categories In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories. Cat may actually be regarded as a 2-category wi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Category of small categories Summary Category_of_small_categories The terminal object is the terminal category or trivial category 1 with a single object and morphism.The category Cat is itself a large category, and therefore not an object of itself. In order to avoid problems analogous to Russell's paradox one cannot ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Axiom of global choice Summary Axiom_of_global_choice In mathematics, specifically in class theories, the axiom of global choice is a stronger variant of the axiom of choice that applies to proper classes of sets as well as sets of sets. Informally it states that one can simultaneously choose an element from every non-... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal polytope Summary Normal_polytope In mathematics, specifically in combinatorial commutative algebra, a convex lattice polytope P is called normal if it has the following property: given any positive integer n, every lattice point of the dilation nP, obtained from P by scaling its vertices by the factor n and taki... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary symmetric polynomial Summary Elementary_symmetric_polynomial In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed as a polynomial in elementary symm... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Power sum symmetric polynomial Summary Power_sum_symmetric_polynomial In mathematics, specifically in commutative algebra, the power sum symmetric polynomials are a type of basic building block for symmetric polynomials, in the sense that every symmetric polynomial with rational coefficients can be expressed as a sum a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fatou's theorem Summary Fatou's_theorem In mathematics, specifically in complex analysis, Fatou's theorem, named after Pierre Fatou, is a statement concerning holomorphic functions on the unit disk and their pointwise extension to the boundary of the disk. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kähler quotient Summary Kähler_quotient In mathematics, specifically in complex geometry, the Kähler quotient of a Kähler manifold X {\displaystyle X} by a Lie group G {\displaystyle G} acting on X {\displaystyle X} by preserving the Kähler structure and with moment map μ: X → g ∗ {\displaystyle \mu :X\to {\mathfrak {g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Robust geometric computation Summary Robust_geometric_computation In mathematics, specifically in computational geometry, geometric nonrobustness is a problem wherein branching decisions in computational geometry algorithms are based on approximate numerical computations, leading to various forms of unreliability inclu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Robust geometric computation Summary Robust_geometric_computation For instance, two-dimensional convex hulls can be computed using predicates that test the sign of quadratic polynomials, and therefore may require twice as many bits of precision within these calculations as the input numbers. When integer arithmetic can... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Subspace identification method Summary Subspace_identification_method In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data. SID does not require that the user parametrizes the system matrices before solvin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equilibrium points Summary Equilibrium_points In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isothermal coordinates Summary Isothermal_coordinates In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric. This means that in isothermal coordinates, the Riemannian metric locally has the form ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isothermal coordinates Summary Isothermal_coordinates Isothermal coordinates on surfaces were first introduced by Gauss. Korn and Lichtenstein proved that isothermal coordinates exist around any point on a two dimensional Riemannian manifold. By contrast, most higher-dimensional manifolds do not admit isothermal coordi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Morse–Bott function Summary Morse–Bott_function In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Morse–Bott function Summary Morse–Bott_function Before Morse, Arthur Cayley and James Clerk Maxwell had developed some of the ideas of Morse theory in the context of topography. Morse originally applied his theory to geodesics (critical points of the energy functional on the space of paths). These techniques were used ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kervaire manifold Summary Kervaire_manifold In mathematics, specifically in differential topology, a Kervaire manifold K 4 n + 2 {\displaystyle K^{4n+2}} is a piecewise-linear manifold of dimension 4 n + 2 {\displaystyle 4n+2} constructed by Michel Kervaire (1960) by plumbing together the tangent bundles of two ( 2 n +... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Rule of proportion Summary Cross-multiplication In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fundamental theorem of Hilbert spaces Summary Fundamental_theorem_of_Hilbert_spaces In mathematics, specifically in functional analysis and Hilbert space theory, the fundamental theorem of Hilbert spaces gives a necessarily and sufficient condition for a Hausdorff pre-Hilbert space to be a Hilbert space in terms of the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vector-valued Hahn–Banach theorems Summary Vector-valued_Hahn–Banach_theorems In mathematics, specifically in functional analysis and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals (which are always valued in the real numbers R {\displays... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topological vector lattice Summary Topological_vector_lattice In mathematics, specifically in functional analysis and order theory, a topological vector lattice is a Hausdorff topological vector space (TVS) X {\displaystyle X} that has a partial order ≤ {\displaystyle \,\leq \,} making it into vector lattice that is po... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ordered topological vector space Summary Ordered_topological_vector_space In mathematics, specifically in functional analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order ≤ making it into an ordered vector space whose p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Amenable Banach algebra Summary Amenable_Banach_algebra In mathematics, specifically in functional analysis, a Banach algebra, A, is amenable if all bounded derivations from A into dual Banach A-bimodules are inner (that is of the form a ↦ a . x − x . a {\displaystyle a\mapsto a.x-x.a} for some x {\displaystyle x} in t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
C* algebra Summary Cstar_algebra In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space wi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
C* algebra Summary Cstar_algebra This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establish a general framework for these algebras, which culminated in a series of papers on ring... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
C* algebra Summary Cstar_algebra Around 1943, the work of Israel Gelfand and Mark Naimark yielded an abstract characterisation of C*-algebras making no reference to operators on a Hilbert space. C*-algebras are now an important tool in the theory of unitary representations of locally compact groups, and are also used i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Saturated family Summary Saturated_family In mathematics, specifically in functional analysis, a family G {\displaystyle {\mathcal {G}}} of subsets a topological vector space (TVS) X {\displaystyle X} is said to be saturated if G {\displaystyle {\mathcal {G}}} contains a non-empty subset of X {\displaystyle X} and if f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Disk algebra Summary Disk_algebra In mathematics, specifically in functional and complex analysis, the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions ƒ: D → C {\displaystyle \mathbb {C} } ,(where D is the open unit disk in the complex plane C {\displaystyle \mathbb {C} } ) that extend... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Disk algebra Summary Disk_algebra By construction the disc algebra is a closed subalgebra of the Hardy space H∞. In contrast to the stronger requirement that a continuous extension to the circle exists, it is a lemma of Fatou that a general element of H∞ can be radially extended to the circle almost everywhere. == Refe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Algebraic surgery theory Summary Surgery_theory In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by John Milnor (1961). Milnor called this technique surgery, while Andrew Wallac... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Algebraic surgery theory Summary Surgery_theory This is closely related to, but not identical with, handlebody decompositions. More technically, the idea is to start with a well-understood manifold M and perform surgery on it to produce a manifold M′ having some desired property, in such a way that the effects on the h... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hydra game Summary Hydra_game In mathematics, specifically in graph theory and number theory, a hydra game is a single-player iterative mathematical game played on a mathematical tree called a hydra where, usually, the goal is to cut off the hydra's "heads" while the hydra simultaneously expands itself. Hydra games can... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary abelian Summary Elementary_abelian In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same order. This common order must be a prime number, and the elementary abelian groups in which the common order is p are a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary abelian Summary Elementary_abelian Here, Z/pZ denotes the cyclic group of order p (or equivalently the integers mod p), and the superscript notation means the n-fold direct product of groups.In general, a (possibly infinite) elementary abelian p-group is a direct sum of cyclic groups of order p. (Note that i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Residue-class-wise affine group Summary Residue-class-wise_affine_group In mathematics, specifically in group theory, residue-class-wise affine groups are certain permutation groups acting on Z {\displaystyle \mathbb {Z} } (the integers), whose elements are bijective residue-class-wise affine mappings. A mapping f: Z →... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Residue-class-wise affine group Summary Residue-class-wise_affine_group Many of them act multiply transitively on Z {\displaystyle \mathbb {Z} } or on subsets thereof. A particularly basic type of residue-class-wise affine permutations are the class transpositions: given disjoint residue classes r 1 ( m 1 ) {\displayst... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quasicyclic group Summary Quasicyclic_group In mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p∞-group, Z(p∞), for a prime number p is the unique p-group in which every element has p different p-th roots. The Prüfer p-groups are countable abelian groups that are important in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Semi-direct product Summary Semidirect_product In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. There are two closely related concepts of semidirect product: an inner semidirect product is a particular way in which a group can be made up of two s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Direct product (group theory) Summary Direct_product_(group_theory) In mathematics, specifically in group theory, the direct product is an operation that takes two groups G and H and constructs a new group, usually denoted G × H. This operation is the group-theoretic analogue of the Cartesian product of sets and is one... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Groups of Lie type Summary Steinberg_group_(Lie_theory) In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phrase group of Lie type do... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Commensurability (group theory) Summary Commensurability_(group_theory) In mathematics, specifically in group theory, two groups are commensurable if they differ only by a finite amount, in a precise sense. The commensurator of a subgroup is another subgroup, related to the normalizer. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generalized homology theory Summary Cohomology_groups In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generalized homology theory Summary Cohomology_groups From its beginning in topology, this idea became a dominant method in the mathematics of the second half of the twentieth century. From the initial idea of homology as a method of constructing algebraic invariants of topological spaces, the range of applications of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coherence theorem Summary Coherency_(homotopy_theory) In mathematics, specifically in homotopy theory and (higher) category theory, coherency is the standard that equalities or diagrams must satisfy when they hold "up to homotopy" or "up to isomorphism". The adjectives such as "pseudo-" and "lax-" are used to refer to ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fibrant object Summary Fibrant_object In mathematics, specifically in homotopy theory in the context of a model category M, a fibrant object A of M is an object that has a fibration to the terminal object of the category. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classifying space Summary Classifying_space In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e., a topological space all of whose homotopy groups are trivial) by a proper free action of G. It has the property that any G... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classifying space Summary Classifying_space This notion is generalized by the notion of classifying topos. However, the rest of this article discusses the more commonly used notion of classifying space up to homotopy. For a discrete group G, BG is, roughly speaking, a path-connected topological space X such that the fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Complete quadrilateral Summary Complete_quadrilateral In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hasse–Arf theorem Summary Hasse–Arf_theorem In mathematics, specifically in local class field theory, the Hasse–Arf theorem is a result concerning jumps of the upper numbering filtration of the Galois group of a finite Galois extension. A special case of it when the residue fields are finite was originally proved by He... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel probability measure Summary Borel_measure In mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets). Some authors require additional restrictions on the measure, as described below. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Trivial measure Summary Trivial_measure In mathematics, specifically in measure theory, the trivial measure on any measurable space (X, Σ) is the measure μ which assigns zero measure to every measurable set: μ(A) = 0 for all A in Σ. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newman's conjecture Summary Newman's_conjecture In mathematics, specifically in number theory, Newman's conjecture is a conjecture about the behavior of the partition function modulo any integer. Specifically, it states that for any integers m and r such that 0 ≤ r ≤ m − 1 {\displaystyle 0\leq r\leq m-1} , the value of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cunningham number Summary Cunningham_number In mathematics, specifically in number theory, a Cunningham number is a certain kind of integer named after English mathematician A. J. C. Cunningham. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binomial number Summary Binomial_number In mathematics, specifically in number theory, a binomial number is an integer which can be obtained by evaluating a homogeneous polynomial containing two terms. It is a generalization of a Cunningham number. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Extremal orders of an arithmetic function Summary Extremal_orders_of_an_arithmetic_function In mathematics, specifically in number theory, the extremal orders of an arithmetic function are best possible bounds of the given arithmetic function. Specifically, if f(n) is an arithmetic function and m(n) is a non-decreasing... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baum–Connes conjecture Summary Baum–Connes_conjecture In mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the K-theory of the reduced C*-algebra of a group and the K-homology of the classifying space of proper actions of that group. The conjecture sets up a corresponden... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baum–Connes conjecture Summary Baum–Connes_conjecture For instance, the surjectivity part implies the Kadison–Kaplansky conjecture for discrete torsion-free groups, and the injectivity is closely related to the Novikov conjecture. The conjecture is also closely related to index theory, as the assembly map μ {\displayst... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hermitian conjugate Summary Hermitian_adjoint In mathematics, specifically in operator theory, each linear operator A {\displaystyle A} on an inner product space defines a Hermitian adjoint (or adjoint) operator A ∗ {\displaystyle A^{*}} on that space according to the rule ⟨ A x , y ⟩ = ⟨ x , A ∗ y ⟩ , {\displaystyle \... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hermitian conjugate Summary Hermitian_adjoint The above definition of an adjoint operator extends verbatim to bounded linear operators on Hilbert spaces H {\displaystyle H} . The definition has been further extended to include unbounded densely defined operators whose domain is topologically dense in - but not necessar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fréchet lattice Summary Fréchet_lattice In mathematics, specifically in order theory and functional analysis, a Fréchet lattice is a topological vector lattice that is also a Fréchet space. Fréchet lattices are important in the theory of topological vector lattices. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Band (order theory) Summary Band_(order_theory) In mathematics, specifically in order theory and functional analysis, a band in a vector lattice X {\displaystyle X} is a subspace M {\displaystyle M} of X {\displaystyle X} that is solid and such that for all S ⊆ M {\displaystyle S\subseteq M} such that x = sup S {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Order convergence Summary Order_convergence In mathematics, specifically in order theory and functional analysis, a filter F {\displaystyle {\mathcal {F}}} in an order complete vector lattice X {\displaystyle X} is order convergent if it contains an order bounded subset (that is, is contained in an interval of the form... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally convex vector lattice Summary Locally_convex_vector_lattice In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in the theory of topological vector lattices. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normed lattice Summary Normed_vector_lattice In mathematics, specifically in order theory and functional analysis, a normed lattice is a topological vector lattice that is also a normed space whose unit ball is a solid set. Normed lattices are important in the theory of topological vector lattices. They are closely rel... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Order summable Summary Order_summable In mathematics, specifically in order theory and functional analysis, a sequence of positive elements ( x i ) i = 1 ∞ {\displaystyle \left(x_{i}\right)_{i=1}^{\infty }} in a preordered vector space X {\displaystyle X} (that is, x i ≥ 0 {\displaystyle x_{i}\geq 0} for all i {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Solid set Summary Solid_set In mathematics, specifically in order theory and functional analysis, a subset S {\displaystyle S} of a vector lattice is said to be solid and is called an ideal if for all s ∈ S {\displaystyle s\in S} and x ∈ X , {\displaystyle x\in X,} if | x | ≤ | s | {\displaystyle |x|\leq |s|} then x ∈ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Solid set Summary Solid_set If S ⊆ X {\displaystyle S\subseteq X} then the ideal generated by S {\displaystyle S} is the smallest ideal in X {\displaystyle X} containing S . {\displaystyle S.} An ideal generated by a singleton set is called a principal ideal in X . {\displaystyle X.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Abstract L-space Summary Abstract_L-space In mathematics, specifically in order theory and functional analysis, an abstract L-space, an AL-space, or an abstract Lebesgue space is a Banach lattice ( X , ‖ ⋅ ‖ ) {\displaystyle (X,\|\cdot \|)} whose norm is additive on the positive cone of X.In probability theory, it mean... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Abstract m-space Summary Abstract_m-space In mathematics, specifically in order theory and functional analysis, an abstract m-space or an AM-space is a Banach lattice ( X , ‖ ⋅ ‖ ) {\displaystyle (X,\|\cdot \|)} whose norm satisfies ‖ sup { x , y } ‖ = sup { ‖ x ‖ , ‖ y ‖ } {\displaystyle \left\|\sup\{x,y\}\right\|=\su... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weak order unit Summary Weak_order_unit In mathematics, specifically in order theory and functional analysis, an element x {\displaystyle x} of a vector lattice X {\displaystyle X} is called a weak order unit in X {\displaystyle X} if x ≥ 0 {\displaystyle x\geq 0} and also for all y ∈ X , {\displaystyle y\in X,} inf { ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quasi-interior point Summary Quasi-interior_point In mathematics, specifically in order theory and functional analysis, an element x {\displaystyle x} of an ordered topological vector space X {\displaystyle X} is called a quasi-interior point of the positive cone C {\displaystyle C} of X {\displaystyle X} if x ≥ 0 {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cone-saturated Summary Cone-saturated In mathematics, specifically in order theory and functional analysis, if C {\displaystyle C} is a cone at 0 in a vector space X {\displaystyle X} such that 0 ∈ C , {\displaystyle 0\in C,} then a subset S ⊆ X {\displaystyle S\subseteq X} is said to be C {\displaystyle C} -saturated ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cone-saturated Summary Cone-saturated {\displaystyle S.} If F {\displaystyle {\mathcal {F}}} is a collection of subsets of X {\displaystyle X} then C := { C: F ∈ F } . {\displaystyle \left_{C}:=\left\{_{C}:F\in {\mathcal {F}}\right\}.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cone-saturated Summary Cone-saturated If T {\displaystyle {\mathcal {T}}} is a collection of subsets of X {\displaystyle X} and if F {\displaystyle {\mathcal {F}}} is a subset of T {\displaystyle {\mathcal {T}}} then F {\displaystyle {\mathcal {F}}} is a fundamental subfamily of T {\displaystyle {\mathcal {T}}} if ever... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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