| {"id":"condensed:profinite:inj-in-prod-f2","label":"inj-in-prod-f2","background_color":"#A3D6FF","border_color":"blue","kind":"ellipse","dep_graph_url":"https://Waschbaar.github.io/ananas-web/dep_graph_document.html","dependencies":[],"nlp_text":"If \\( S \\) is a profinite set, then the continuous map \\( S\\to \\prod _{f\\in \\mathrm{Cont}(S, \\mathbb {F}_{2})} \\mathbb {F}_{2} \\) determined by the maps \\( f\\in \\mathrm{Cont}(S, \\mathbb {F}_{2}) \\) is injective.","doc_url":null,"latex_link":"sect0001.html#condensed:profinite:inj-in-prod-f2","lean_link":null,"lean_decl_name":"inj-in-prod-f2","kind_description":"theorems and lemmas","status_from_color":"ready_to_formalize","lookup_in_mathlib4v4.22.0":true,"found_in_mathlib4v4.22.0":false,"proof_status":"nlp_only"} |
| {"id":"profinite:noebeling","label":"noebeling","background_color":"#A3D6FF","border_color":"blue","kind":"ellipse","dep_graph_url":"https://Waschbaar.github.io/ananas-web/dep_graph_document.html","dependencies":[],"nlp_text":"If \\( S \\) is a profinite set, then the abelian group \\( \\mathrm{Cont}(S, \\mathbb {Z}) \\) is free.","doc_url":null,"latex_link":"sect0001.html#profinite:noebeling","lean_link":null,"lean_decl_name":"noebeling","kind_description":"theorems and lemmas","status_from_color":"ready_to_formalize","lookup_in_mathlib4v4.22.0":true,"found_in_mathlib4v4.22.0":false,"proof_status":"nlp_only"} |
| {"id":"condensed:profinite:extend-loc-const-from-closed","label":"extend-loc-const-from-closed","background_color":"#A3D6FF","border_color":"blue","kind":"ellipse","dep_graph_url":"https://Waschbaar.github.io/ananas-web/dep_graph_document.html","dependencies":[],"nlp_text":"Suppose that \\( S \\) is a profinite set, \\( T\\subset S \\) a closed subset and \\( M \\) a discrete topological space. Then the map \\( \\mathrm{Cont}(S, M)\\to \\mathrm{Cont}(T, M) \\) given by precomposition with the inclusion map is surjective.","doc_url":null,"latex_link":"sect0001.html#condensed:profinite:extend-loc-const-from-closed","lean_link":null,"lean_decl_name":"extend-loc-const-from-closed","kind_description":"theorems and lemmas","status_from_color":"ready_to_formalize","lookup_in_mathlib4v4.22.0":true,"found_in_mathlib4v4.22.0":false,"proof_status":"nlp_only"} |
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