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https://en.wikipedia.org/wiki/Fully%20normalized%20subgroup | In mathematics, in the field of group theory, a subgroup of a group is said to be fully normalized if every automorphism of the subgroup lifts to an inner automorphism of the whole group. Another way of putting this is that the natural embedding from the Weyl group of the subgroup to its automorphism group is surjectiv... |
https://en.wikipedia.org/wiki/CEP%20subgroup | In mathematics, in the field of group theory, a subgroup of a group is said to have the Congruence Extension Property or to be a CEP subgroup if every congruence on the subgroup lifts to a congruence of the whole group. Equivalently, every normal subgroup of the subgroup arises as the intersection with the subgroup of ... |
https://en.wikipedia.org/wiki/William%20S.%20Massey | William Schumacher Massey (August 23, 1920 – June 17, 2017) was an American mathematician, known for his work in algebraic topology. The Massey product is named for him. He worked also on the formulation of spectral sequences by means of exact couples, and wrote several textbooks, including A Basic Course in Algebraic ... |
https://en.wikipedia.org/wiki/Retract%20%28group%20theory%29 | In mathematics, in the field of group theory, a subgroup of a group is termed a retract if there is an endomorphism of the group that maps surjectively to the subgroup and is the identity on the subgroup. In symbols, is a retract of if and only if there is an endomorphism such that for all and for all .
The endo... |
https://en.wikipedia.org/wiki/Norm%20%28group%29 | In mathematics, in the field of group theory, the norm of a group is the intersection of the normalizers of all its subgroups. This is also termed the Baer norm, after Reinhold Baer.
The following facts are true for the Baer norm:
It is a characteristic subgroup.
It contains the center of the group.
It is containe... |
https://en.wikipedia.org/wiki/Demography%20of%20London | The demography of London is analysed by the Office for National Statistics and data is produced for each of the Greater London wards, the City of London and the 32 London boroughs, the Inner London and Outer London statistical sub-regions, each of the Parliamentary constituencies in London, and for all of Greater Londo... |
https://en.wikipedia.org/wiki/AP%20Statistics | Advanced Placement (AP) Statistics (also known as AP Stats) is a college-level high school statistics course offered in the United States through the College Board's Advanced Placement program. This course is equivalent to a one semester, non-calculus-based introductory college statistics course and is normally offered... |
https://en.wikipedia.org/wiki/Mathematics%20%28disambiguation%29 | Mathematics is a field of knowledge.
Mathematics may also refer to:
Music
Mathematics (album), a 1985 album by Melissa Manchester
"Mathematics" (Cherry Ghost song), a song by Cherry Ghost
"Mathematics" (Mos Def song), a song by Mos Def
Mathematics, an EP by The Servant
"Mathematics", a song by bbno$
"Mathematic... |
https://en.wikipedia.org/wiki/Proceedings%20of%20the%20American%20Mathematical%20Society | Proceedings of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages.
According to the Journal Citation Reports, the journal has a 2018 impact factor of 0.813.
Sco... |
https://en.wikipedia.org/wiki/American%20Journal%20of%20Mathematics | The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.
History
The American Journal of Mathematics is the oldest continuously published mathematical journal in the United States, established in 1878 at the Johns Hopkins University by James Joseph Sylves... |
https://en.wikipedia.org/wiki/Conjugacy-closed%20subgroup | In mathematics, in the field of group theory, a subgroup of a group is said to be conjugacy-closed if any two elements of the subgroup that are conjugate in the group are also conjugate in the subgroup.
An alternative characterization of conjugacy-closed normal subgroups is that all class automorphisms of the whole gr... |
https://en.wikipedia.org/wiki/Weakly%20normal%20subgroup | In mathematics, in the field of group theory, a subgroup of a group is said to be weakly normal if whenever , we have .
Every pronormal subgroup is weakly normal.
References
Subgroup properties |
https://en.wikipedia.org/wiki/Degen%27s%20eight-square%20identity | In mathematics, Degen's eight-square identity establishes that the product of two numbers, each of which is a sum of eight squares, is itself the sum of eight squares.
Namely:
First discovered by Carl Ferdinand Degen around 1818, the identity was independently rediscovered by John Thomas Graves (1843) and Arthur Cayle... |
https://en.wikipedia.org/wiki/Fermat%20%28computer%20algebra%20system%29 | Fermat (named after Pierre de Fermat) is a program developed by Prof. Robert H. Lewis of Fordham University. It is a computer algebra system, in which items being computed can be integers (of arbitrary size), rational numbers, real numbers, complex numbers, modular numbers, finite field elements, multivariable polynomi... |
https://en.wikipedia.org/wiki/J.%20Hyam%20Rubinstein | Joachim Hyam Rubinstein FAA (born 7 March 1948, in Melbourne) an Australian top mathematician specialising in low-dimensional topology; he is currently serving as an honorary professor in the Department of Mathematics and Statistics at the University of Melbourne, having retired in 2019.
He has spoken and written wi... |
https://en.wikipedia.org/wiki/Genocchi%20number | In mathematics, the Genocchi numbers Gn, named after Angelo Genocchi, are a sequence of integers that satisfy the relation
The first few Genocchi numbers are 0, −1, −1, 0, 1, 0, −3, 0, 17 , see .
Properties
The generating function definition of the Genocchi numbers implies that they are rational numbers. In fact,... |
https://en.wikipedia.org/wiki/Moment%20matrix | In mathematics, a moment matrix is a special symmetric square matrix whose rows and columns are indexed by monomials. The entries of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices.)
Moment matrices play an important role in polynomial fitting, polynomial optimization (since positi... |
https://en.wikipedia.org/wiki/Ideal%20point | In hyperbolic geometry, an ideal point, omega point or point at infinity is a well-defined point outside the hyperbolic plane or space.
Given a line l and a point P not on l, right- and left-limiting parallels to l through P converge to l at ideal points.
Unlike the projective case, ideal points form a boundary, not a... |
https://en.wikipedia.org/wiki/Cantor%20cube | In mathematics, a Cantor cube is a topological group of the form {0, 1}A for some index set A. Its algebraic and topological structures are the group direct product and product topology over the cyclic group of order 2 (which is itself given the discrete topology).
If A is a countably infinite set, the corresponding C... |
https://en.wikipedia.org/wiki/Tijdeman%27s%20theorem | In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in integers x, y, n, m of the exponential diophantine equation
for exponents n and m greater than one, is finite.
History
The theorem was proven by Dutch number theorist R... |
https://en.wikipedia.org/wiki/Israel%20Nathan%20Herstein | Israel Nathan Herstein (March 28, 1923 – February 9, 1988) was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
Education and career
Herstein was born in Lublin, Poland,... |
https://en.wikipedia.org/wiki/%27t%20Hooft%20symbol | The t Hooft symbol is a collection of numbers which allows one to express the generators of the SU(2) Lie algebra in terms of the generators of Lorentz algebra. The symbol is a blend between the Kronecker delta and the Levi-Civita symbol. It was introduced by Gerard 't Hooft. It is used in the construction of the BPST ... |
https://en.wikipedia.org/wiki/Orthogonal%20coordinates | In mathematics, orthogonal coordinates are defined as a set of coordinates in which the coordinate hypersurfaces all meet at right angles (note that superscripts are indices, not exponents). A coordinate surface for a particular coordinate is the curve, surface, or hypersurface on which is a constant. For example, ... |
https://en.wikipedia.org/wiki/Star%20Flyer%20%28Tivoli%20Gardens%29 | Star Flyer () is a carousel-meets-watchtower style amusement ride in Tivoli Gardens, Copenhagen, Denmark. It was manufactured by Funtime and opened in May 2006.
Statistics
Height
Platform diameter
Chairs 12 (2 seats each)
Capacity circa 960 passengers/hour
Maximum rotation speed
Maximum vertical speed
References
... |
https://en.wikipedia.org/wiki/Elliptic%20coordinate%20system | In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci and are generally taken to be fixed at and , respectively, on the -axis of the Cartesian coordinate system.
Basic definition
The most commo... |
https://en.wikipedia.org/wiki/Hopf%20conjecture | In mathematics, Hopf conjecture may refer to one of several conjectural statements from differential geometry and topology attributed to Heinz Hopf.
Positively or negatively curved Riemannian manifolds
The Hopf conjecture is an open problem in global Riemannian geometry. It goes back to questions of Heinz Hopf from ... |
https://en.wikipedia.org/wiki/Parabolic%20cylindrical%20coordinates | In mathematics, parabolic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional parabolic coordinate system in the
perpendicular -direction. Hence, the coordinate surfaces are confocal parabolic cylinders. Parabolic cylindrical coordinates have fo... |
https://en.wikipedia.org/wiki/Tsuruichi%20Hayashi | was a Japanese mathematician and historian of Japanese mathematics. He was born in Tokushima, Japan.
He was the founder of the Tohoku Mathematical Journal.
References
Further reading
External links
The Extremal Chords of an Oval, by TSURUICHI HAYASHI, Sendai.
A Remark on the integral Equation solved by Mr. Hiraka... |
https://en.wikipedia.org/wiki/Sine%20and%20cosine | In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypot... |
https://en.wikipedia.org/wiki/Weyl%20character%20formula | In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights. It was proved by . There is a closely related formula for the character of an irreducible representation of a semisimple Lie algebra. In W... |
https://en.wikipedia.org/wiki/Symmetry%20set | In geometry, the symmetry set is a method for representing the local symmetries of a curve, and can be used as a method for representing the shape of objects by finding the topological skeleton. The medial axis, a subset of the symmetry set is a set of curves which roughly run along the middle of an object.
In 2 dimen... |
https://en.wikipedia.org/wiki/Normal%20measure | In set theory, a normal measure is a measure on a measurable cardinal κ such that the equivalence class of the identity function on κ maps to κ itself in the ultrapower construction. Equivalently, if f:κ→κ is such that f(α)<α for most α<κ, then there is a β<κ such that f(α)=β for most α<κ. (Here, "most" means that the ... |
https://en.wikipedia.org/wiki/Probabilistic%20logic | Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A difficulty of probabilistic logics is their tendency to multiply the computat... |
https://en.wikipedia.org/wiki/Critical%20pair | In mathematics, a critical pair may refer to:
Critical pair (term rewriting), terms resulting from two overlapping rules in a term rewriting system
Critical pair (order theory), two incomparable elements of a partial order that could be made comparable without changing any other relation in the partial order
The pair o... |
https://en.wikipedia.org/wiki/Dependency%20graph | In mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other. It is possible to derive an evaluation order or the absence of an evaluation order that respects the given dependencies from the dependency graph.
Definition... |
https://en.wikipedia.org/wiki/Conway%20polyhedron%20notation | In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations.
Conway and Hart extended the idea of using operators, like truncation as defined by Kepler, to build related polyhedra ... |
https://en.wikipedia.org/wiki/Colorado%20Model%20Content%20Standards | The Colorado Model Content Standards were a set of curriculum standards for teaching civics, dance, economics, foreign language, geography, history, mathematics, music, physical education, reading and writing, science, theatre, and visual arts.
Of the 13 standards only three (mathematics, reading and writing, and scie... |
https://en.wikipedia.org/wiki/Apollonian%20circles | In geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. They were discovered by Apollonius of Perga, a renowned Greek geometer.
Defin... |
https://en.wikipedia.org/wiki/257-gon | In Geometry, 257-gon, also known broadly as the Dihectapentacontakaiheptagon, is a polygon with 257 sides. The sum of the interior angles of any non-self-intersecting 257-gon is 45,900°.
Regular 257-gon
The area of a regular 257-gon is (with )
A whole regular 257-gon is not visually discernible from a circle, and it... |
https://en.wikipedia.org/wiki/65537-gon | In geometry, a 65537-gon is a polygon with 65,537 (216 + 1) sides. The sum of the interior angles of any non–self-intersecting is 11796300°.
Regular 65537-gon
The area of a regular is (with )
A whole regular is not visually discernible from a circle, and its perimeter differs from that of the circumscribed circle ... |
https://en.wikipedia.org/wiki/Vampirium | Vampirium is the twenty-seventh book of the award-winning Lone Wolf series of gamebooks created by Joe Dever.
Gameplay
Lone Wolf books rely on a combination of thought and luck. Certain statistics such as combat skill and endurance attributes are determined randomly before play (reading). The player is then allowed ... |
https://en.wikipedia.org/wiki/Macdonald%20identities | In mathematics, the Macdonald identities are some infinite product identities associated to affine root systems, introduced by . They include as special cases the Jacobi triple product identity, Watson's quintuple product identity, several identities found by , and a 10-fold product identity found by .
and pointed ... |
https://en.wikipedia.org/wiki/Peter%20Ozsv%C3%A1th | Peter Steven Ozsváth (born October 20, 1967) is a professor of mathematics at Princeton University. He created, along with Zoltán Szabó, Heegaard Floer homology, a homology theory for 3-manifolds.
Education
Ozsváth received his Ph.D. from Princeton in 1994 under the supervision of John Morgan; his dissertation was en... |
https://en.wikipedia.org/wiki/Suslin%20tree | In mathematics, a Suslin tree is a tree of height ω1 such that
every branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin.
Every Suslin tree is an Aronszajn tree.
The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (show... |
https://en.wikipedia.org/wiki/Trail%20of%20the%20Wolf | Trail of the Wolf is the twenty-fifth book of the Lone Wolf book series created by Joe Dever.
Gameplay
Lone Wolf books rely on a combination of thought and luck. Certain statistics such as combat skill and endurance attributes are determined randomly before play (reading). The player is then allowed to choose which ... |
https://en.wikipedia.org/wiki/Rune%20War | Rune War is the twenty-fourth book of the award-winning Lone Wolf book series created by Joe Dever.
Gameplay
Lone Wolf books rely on a combination of thought and luck. Certain statistics such as combat skill and endurance attributes are determined randomly before play (reading). The player is then allowed to choose ... |
https://en.wikipedia.org/wiki/Mydnight%27s%20Hero | Mydnight's Hero is the twenty-third book of the award-winning Lone Wolf book series created by Joe Dever.
Gameplay
Lone Wolf books rely on a combination of thought and luck. Certain statistics such as combat skill and endurance attributes are determined randomly before play (reading). The player is then allowed to c... |
https://en.wikipedia.org/wiki/Bernhard%20Neumann | Bernhard Hermann Neumann (15 October 1909 – 21 October 2002) was a German-born British-Australian mathematician, who was a leader in the study of group theory.
Early life and education
After gaining a D.Phil. from Friedrich-Wilhelms Universität in Berlin in 1932 he earned a Ph.D. at the University of Cambridge in 193... |
https://en.wikipedia.org/wiki/Monster%20vertex%20algebra | The monster vertex algebra (or moonshine module) is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky, and Arne Meurman. R. Borcherds used it to prove the monstrous moonshine conjectures, by applying the Goddard–Thorn theorem of string theory to construct the monster Li... |
https://en.wikipedia.org/wiki/James%20Lepowsky | James Lepowsky (born July 5, 1944) is a professor of mathematics at Rutgers University, New Jersey. Previously he taught at Yale University. He received his Ph.D. from Massachusetts Institute of Technology in 1970 where his advisors were Bertram Kostant and Sigurdur Helgason. Lepowsky graduated from Stuyvesant High Sch... |
https://en.wikipedia.org/wiki/Arne%20Meurman | Arne Meurman (born 6 April 1956) is a Swedish mathematician working on finite groups and vertex operator algebras. Currently, he is a professor at Lund University.
He is best known for constructing the monster vertex algebra together with Igor Frenkel and James Lepowsky.
He is interested in chess.
Publications
Igo... |
https://en.wikipedia.org/wiki/Osem | Osem may refer to:
Osem (mathematics) – algorithm for image reconstruction in nuclear medical imaging
Osem (company) – Israeli food corporation
Orquesta Sinfonica del Estado de Mexico, an official State symphony orchestra in Mexico. |
https://en.wikipedia.org/wiki/Robert%20Griess | Robert Louis Griess, Jr. (born 1945, Savannah, Georgia) is a mathematician working on finite simple groups and vertex algebras. He is currently the John Griggs Thompson Distinguished University Professor of mathematics at University of Michigan.
Education
Griess developed a keen interest in mathematics prior to enter... |
https://en.wikipedia.org/wiki/O%27Leary%2C%20Prince%20Edward%20Island | O'Leary is a town located in Prince County, Prince Edward Island. Its population in the 2016 Census was 815 people.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, O'Leary had a population of living in of its total private dwellings, a change of from its 2016 population of . With a ... |
https://en.wikipedia.org/wiki/Sofya%20Yanovskaya | Sofya Aleksandrovna Yanovskaya (also Janovskaja; ; 31 January 1896 – 24 October 1966) was a Soviet mathematician and historian, specializing in the history of mathematics, mathematical logic, and philosophy of mathematics. She is best known for her efforts in restoring the research of mathematical logic in the Soviet U... |
https://en.wikipedia.org/wiki/Josip%20Belu%C5%A1i%C4%87 | Josip Belušić (March 12, 1847 – January 8, 1905) was a Croatian inventor and professor of physics and mathematics. He was born in the small settlement of Županići, in the region of Labin, Istria, and schooled in Pazin and Koper. Belušić continued his studies in Vienna, later resettling in Trieste before coming back to ... |
https://en.wikipedia.org/wiki/Constructive%20set%20theory | Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory.
The same first-order language with "" and "" of classical set theory is usually used, so this is not to be confused with a constructive types approach.
On the other hand, some constructive theo... |
https://en.wikipedia.org/wiki/Absolute%20value%20%28algebra%29 | In algebra, an absolute value (also called a valuation, magnitude, or norm, although "norm" usually refers to a specific kind of absolute value on a field) is a function which measures the "size" of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping... |
https://en.wikipedia.org/wiki/Paul%20Hoffert | Paul Matthew Hoffert, LLD, CM (born 22 September 1943, in Brooklyn, New York) is a recording artist, performer, media music composer, author, academic, and corporate executive. He studied mathematics and physics at the University of Toronto. He later studied music composition with Gordon Delamont. In 1969, the 26-year-... |
https://en.wikipedia.org/wiki/Belt%20transect | Belt transects are used in biology, more specifically in biostatistics, to estimate the distribution of organisms in relation to a certain area, such as the seashore or a meadow.
The belt transect method is similar to the line transect method but gives information on abundance as well as presence, or absence of specie... |
https://en.wikipedia.org/wiki/Pauli%20group | In physics and mathematics, the Pauli group on 1 qubit is the 16-element matrix group consisting of the 2 × 2 identity matrix and all of the Pauli matrices
,
together with the products of these matrices with the factors and :
.
The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfg... |
https://en.wikipedia.org/wiki/National%20Science%20%26%20Mathematics%20Access%20to%20Retain%20Talent%20Grant | The National Science and Mathematics Access to Retain Talent (SMART) Grant was a need based federal grant that was awarded to undergraduate students in their third and fourth year of undergraduate studies. The National SMART grant was introduced to help maintain the edge that United States has in the fields of Science ... |
https://en.wikipedia.org/wiki/Evidential%20reasoning | Evidential reason or evidential reasoning may refer to:
Probabilistic logic, a combination of the capacity of probability theory to handle uncertainty with the capacity of deductive logic to exploit structure
"Evidential reason", a type of reason (argument) in contrast to an "explanatory reason"
Evidential reasonin... |
https://en.wikipedia.org/wiki/SMART%20Defense%20Scholarship%20Program | The Science, Mathematics, And Research For Transformation (SMART) Defense Scholarship Program was tested as a program in 2005 under the Air
Force Office of Scientific Research. SMART was fully established by the National Defense Authorization Act for fiscal year 2006, and was assigned to the Navy Postgraduate School ... |
https://en.wikipedia.org/wiki/Singapore%20Mathematical%20Olympiad | The Singapore Mathematical Olympiad (SMO) is a mathematics competition organised by the Singapore Mathematical Society. It comprises three sections, Junior, Senior and Open, each of which is open to all pre-university students studying in Singapore who meet the age requirements for the particular section. The competiti... |
https://en.wikipedia.org/wiki/Jonathan%20Partington | Jonathan Richard Partington (born 4 February 1955) is an English mathematician who is Emeritus Professor of pure mathematics at the University of Leeds.
Education
Professor Partington was educated at Gresham's School, Holt, and Trinity College, Cambridge, where he completed his PhD thesis entitled "Numerical ranges an... |
https://en.wikipedia.org/wiki/Metacompact%20space | In the mathematical field of general topology, a topological space is said to be metacompact if every open cover has a point-finite open refinement. That is, given any open cover of the topological space, there is a refinement that is again an open cover with the property that every point is contained only in finitely ... |
https://en.wikipedia.org/wiki/Orthocompact%20space | In mathematics, in the field of general topology, a topological space is said to be orthocompact if every open cover has an interior-preserving open refinement.
That is, given an open cover of the topological space, there is a refinement that is also an open cover, with the further property that at any point, the inte... |
https://en.wikipedia.org/wiki/Supercompact%20space | In mathematics, in the field of topology, a topological space is called supercompact if there is a subbasis such that every open cover of the topological space from elements of the subbasis has a subcover with at most two subbasis elements. Supercompactness and the related notion of superextension was introduced by J.... |
https://en.wikipedia.org/wiki/Siegel%E2%80%93Walfisz%20theorem | In analytic number theory, the Siegel–Walfisz theorem was obtained by Arnold Walfisz as an application of a theorem by Carl Ludwig Siegel to primes in arithmetic progressions. It is a refinement both of the prime number theorem and of Dirichlet's theorem on primes in arithmetic progressions.
Statement
Define
where d... |
https://en.wikipedia.org/wiki/Pseudonormal%20space | In mathematics, in the field of topology, a topological space is said to be pseudonormal if given two disjoint closed sets in it, one of which is countable, there are disjoint open sets containing them. Note the following:
Every normal space is pseudonormal.
Every pseudonormal space is regular.
An example of a pseud... |
https://en.wikipedia.org/wiki/Collectionwise%20Hausdorff%20space | In mathematics, in the field of topology, a topological space is said to be collectionwise Hausdorff if given any closed discrete subset of , there is a pairwise disjoint family of open sets with each point of the discrete subset contained in exactly one of the open sets.
Here a subset being discrete has the usual ... |
https://en.wikipedia.org/wiki/Volterra%20space | In mathematics, in the field of topology, a topological space is said to be a Volterra space if any finite intersection of dense Gδ subsets is dense. Every Baire space is Volterra, but the converse is not true. In fact, any metrizable Volterra space is Baire.
The name refers to a paper of Vito Volterra in which he use... |
https://en.wikipedia.org/wiki/A-paracompact%20space | In mathematics, in the field of topology, a topological space is said to be a-paracompact if every open cover of the space has a locally finite refinement. In contrast to the definition of paracompactness, the refinement is not required to be open.
Every paracompact space is a-paracompact, and in regular spaces the tw... |
https://en.wikipedia.org/wiki/Perfect%20set | In general topology, a subset of a topological space is perfect if it is closed and has no isolated points. Equivalently: the set is perfect if , where denotes the set of all limit points of , also known as the derived set of .
In a perfect set, every point can be approximated arbitrarily well by other points from ... |
https://en.wikipedia.org/wiki/Bombieri%27s%20theorem | Bombieri's theorem may refer to:
Bombieri–Vinogradov theorem, a result in analytic number theory
Schneider–Lang theorem for Bombieri's theorem on transcendental numbers |
https://en.wikipedia.org/wiki/Door%20space | In mathematics, specifically in the field of topology, a topological space is said to be a door space if every subset is open or closed (or both). The term comes from the introductory topology mnemonic that "a subset is not like a door: it can be open, closed, both, or neither".
Properties and examples
Every door sp... |
https://en.wikipedia.org/wiki/Richard%20S.%20Kayne | Richard Stanley Kayne is Professor of Linguistics in the Linguistics Department at New York University.
Born in 1944, after receiving an A.B. in mathematics from Columbia College, New York City in 1964, he studied linguistics at the Massachusetts Institute of Technology, receiving his Ph.D. in 1969. He then taught at ... |
https://en.wikipedia.org/wiki/Pseudocompact%20space | In mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded. Many authors include the requirement that the space be completely regular in the definition of pseudocompactness. Pseudocompact spaces were defined by Edwin Hewitt in 194... |
https://en.wikipedia.org/wiki/Realcompact%20space | In mathematics, in the field of topology, a topological space is said to be realcompact if it is completely regular Hausdorff and it contains every point of its Stone–Čech compactification which is real (meaning that the quotient field at that point of the ring of real functions is the reals). Realcompact spaces have a... |
https://en.wikipedia.org/wiki/Locally%20Hausdorff%20space | In mathematics, in the field of topology, a topological space is said to be locally Hausdorff if every point has a neighbourhood that is a Hausdorff space under the subspace topology.
Examples and sufficient conditions
Every Hausdorff space is locally Hausdorff.
There are locally Hausdorff spaces where a sequence h... |
https://en.wikipedia.org/wiki/Mesocompact%20space | In mathematics, in the field of general topology, a topological space is said to be mesocompact if every open cover has a compact-finite open refinement. That is, given any open cover, we can find an open refinement with the property that every compact set meets only finitely many members of the refinement.
The follow... |
https://en.wikipedia.org/wiki/Shrinking%20space | In mathematics, in the field of topology, a topological space is said to be a shrinking space if every open cover admits a shrinking. A shrinking of an open cover is another open cover indexed by the same indexing set, with the property that the closure of each open set in the shrinking lies inside the corresponding or... |
https://en.wikipedia.org/wiki/Hemicompact%20space | In mathematics, in the field of topology, a topological space is said to be hemicompact if it has a sequence of compact subsets such that every compact subset of the space lies inside some compact set in the sequence. Clearly, this forces the union of the sequence to be the whole space, because every point is compact a... |
https://en.wikipedia.org/wiki/Dice%20notation | Dice notation (also known as dice algebra, common dice notation, RPG dice notation, and several other titles) is a system to represent different combinations of dice in wargames and tabletop role-playing games using simple algebra-like notation such as d8+2.
Standard notation
In most tabletop role-playing games, die... |
https://en.wikipedia.org/wiki/Cochrane%20Lake%2C%20Alberta | Cochrane Lake is a hamlet in southern Alberta under the jurisdiction of Rocky View County. Statistics Canada also recognizes a smaller portion of the hamlet as a designated place under the name of Cochrane Lake Subdivision.
Cochrane Lake is located approximately 45 km (23 mi) northwest of the City of Calgary and 1.6 ... |
https://en.wikipedia.org/wiki/List%20of%20NHL%20statistical%20leaders%20by%20country%20of%20birth | This is a list of National Hockey League statistical leaders by country of birth, sorted by total points. The top ten players from each country are included. Statistics are current through the end of the 2022–23 NHL season and players currently playing in the National Hockey League are marked in boldface.
All players ... |
https://en.wikipedia.org/wiki/Cuzick%E2%80%93Edwards%20test | In statistics, the Cuzick–Edwards test is a significance test whose aim is to detect the possible clustering of sub-populations within a clustered or non-uniformly-spread overall population. Possible applications of the test include examining the spatial clustering of childhood leukemia and lymphoma within the general ... |
https://en.wikipedia.org/wiki/Rearrangement | Rearrangement may refer to:
Chemistry
Rearrangement reaction
Mathematics
Rearrangement inequality
The Riemann rearrangement theorem, also called the Riemann series theorem
see also Lévy–Steinitz theorem
A permutation of the terms of a conditionally convergent series
Genetics
Chromosomal rearrangements, suc... |
https://en.wikipedia.org/wiki/Bitopological%20space | In mathematics, a bitopological space is a set endowed with two topologies. Typically, if the set is and the topologies are and then the bitopological space is referred to as . The notion was introduced by J. C. Kelly in the study of quasimetrics, i.e. distance functions that are not required to be symmetric.
Conti... |
https://en.wikipedia.org/wiki/Stinespring%20dilation%20theorem | In mathematics, Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring, is a result from operator theory that represents any completely positive map on a C*-algebra A as a composition of two completely positive maps each of which has a special form:
A *-repr... |
https://en.wikipedia.org/wiki/Free-standing%20Mathematics%20Qualifications | Free-standing Mathematics Qualifications (FSMQ) are a suite of mathematical qualifications available at levels 1 to 3 in the National Qualifications Framework – Foundation, Intermediate and Advanced.
Educational standard
They bridge a gap between GCSE and A-Level Mathematics. The advanced course is especially ideal fo... |
https://en.wikipedia.org/wiki/Contact%20process%20%28mathematics%29 | The contact process is a stochastic process used to model population growth on the set of sites of a graph in which occupied sites become vacant at a constant rate, while vacant sites become occupied at a rate proportional to the number of occupied neighboring sites. Therefore, if we denote by the proportionality con... |
https://en.wikipedia.org/wiki/James%20Stewart%20%28mathematician%29 | James Drewry Stewart, (March 29, 1941December 3, 2014) was a Canadian mathematician, violinist, and professor emeritus of mathematics at McMaster University. Stewart is best known for his series of calculus textbooks used for high school, college, and university level courses.
Career
Stewart received his master of sc... |
https://en.wikipedia.org/wiki/Manjul%20Bhargava | Manjul Bhargava (born 8 August 1974) is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds Adjunct Professorships at the Tata Institute of Fundamental Research, the In... |
https://en.wikipedia.org/wiki/Isodynamic%20point | In Euclidean geometry, the isodynamic points of a triangle are points associated with the triangle, with the properties that an inversion centered at one of these points transforms the given triangle into an equilateral triangle, and that the distances from the isodynamic point to the triangle vertices are inversely pr... |
https://en.wikipedia.org/wiki/Overlap%20%28term%20rewriting%29 | In mathematics, computer science and logic, overlap, as a property of the reduction rules in term rewriting system, describes a situation where a number of different reduction rules specify potentially contradictory ways of reducing a reducible expression, also known as a redex, within a term.
More precisely, if a num... |
https://en.wikipedia.org/wiki/Weber%27s%20theorem%20%28Algebraic%20curves%29 | In mathematics, Weber's theorem, named after Heinrich Martin Weber, is a result on algebraic curves. It states the following.
Consider two non-singular curves C and having the same genus g > 1. If there is a rational correspondence φ between C and , then φ is a birational transformation.
References
Further reading... |
https://en.wikipedia.org/wiki/Heteroclinic%20cycle | In mathematics, a heteroclinic cycle is an invariant set in the phase space of a dynamical system. It is a topological circle of equilibrium points and connecting heteroclinic orbits. If a heteroclinic cycle is asymptotically stable, approaching trajectories spend longer and longer periods of time in a neighbourhood of... |
https://en.wikipedia.org/wiki/Eric%20Lengyel | Eric Lengyel is a computer scientist specializing in game engine development, computer graphics, and geometric algebra. He holds a Ph.D. in computer science from the University of California, Davis and a master's degree in mathematics from Virginia Tech.
Lengyel is an expert in font rendering technology for 3D applica... |
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