翻訳と辞書 Words near each other ・ Pseudochromis dilectus ・ Pseudochromis elongatus ・ Pseudochromis flammicauda ・ Pseudochromis flavivertex ・ Pseudochromis fridmani ・ Pseudochromis fuscus ・ Pseudochromis porphyreus ・ Pseudochromis sankeyi ・ Pseudochromis springeri ・ Pseudochromis steenei ・ Pseudochromis veliferus ・ Pseudochropleura ・ Pseudochrysops ・ Pseudociboria ・ Pseudociliate ・ Pseudocircle ・ Pseudoclanis ・ Pseudoclanis abyssinicus ・ Pseudoclanis aequabilis ・ Pseudoclanis axis ・ Pseudoclanis biokoensis ・ Pseudoclanis canui ・ Pseudoclanis diana ・ Pseudoclanis evestigata ・ Pseudoclanis kakamegae ・ Pseudoclanis kenyae ・ Pseudoclanis occidentalis ・ Pseudoclanis postica ・ Pseudoclanis somaliae ・ Pseudoclanis tomensis Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pseudocircle ： ウィキペディア英語版 Pseudocircle The pseudocircle is the finite topological space ''X'' consisting of four distinct points with the following non-Hausdorff topology: :$\backslash left\backslash ,\backslash ,\backslash ,\backslash ,\backslash ,\backslash emptyset\backslash right\backslash \}$. This topology corresponds to the partial order ''X'' is highly pathological from the usual viewpoint of general topology as it fails to satisfy any separation axiom besides T0. However, from the viewpoint of algebraic topology ''X'' has the remarkable property that it is indistinguishable from the circle ''S''1. More precisely the continuous map ''f'' from ''S''1 to ''X'' (where we think of ''S''1 as the unit circle in R2) given by : is a weak homotopy equivalence, that is ''f'' induces an isomorphism on all homotopy groups. It follows (proposition 4.21 in Hatcher) that ''f'' also induces an isomorphism on singular homology and cohomology and more generally an isomorphism on all ordinary or extraordinary homology and cohomology theories (e.g., K-theory). This can be proved using the following observation. Like ''S''1, ''X'' is the union of two contractible open sets and whose intersection is also the union of two disjoint contractible open sets and . So like ''S''1, the result follows from the groupoid Seifert-van Kampen Theorem, as in the book "Topology and Groupoids". More generally McCord has shown that for any finite simplicial complex ''K'', there is a finite topological space ''X''''K'' which has the same weak homotopy type as the geometric realization |''K''| of ''K''. More precisely there is a functor, taking ''K'' to ''X''''K'', from the category of finite simplicial complexes and simplicial maps and a natural weak homotopy equivalence from |''K''| to ''X''''K''. == References == # # ''(Algebraic Topology )'', by Allen Hatcher, ''Cambridge University Press'', 2002. # Ronald Brown, ''("Topology and Groupoids" )'', Bookforce (2006). Available from amazon. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pseudocircle」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.