翻訳と辞書 Words near each other ・ Particle shower ・ Particle size ・ Particle size (disambiguation) ・ Particle size analysis ・ Partial-matching Meet-in-the-Middle attack ・ Partial-order planning ・ Partialism ・ Partially Buried Woodshed ・ Partially disclosed principal ・ Partially guyed tower ・ Partially observable Markov decision process ・ Partially observable system ・ Partially ordered group ・ Partially ordered ring ・ Partially ordered set ・ Partially ordered space ・ Partially selective school (England) ・ PartiallyClips ・ Partible inheritance ・ Partible paternity ・ Partibrejkers ・ Partibrejkers discography ・ Partibrejkers I ・ Partibrejkers II ・ Partibrejkers III ・ ParticipACTION ・ Participant evolution ・ Participant Media ・ Participant observation ・ Participants in Operation Enduring Freedom 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 Partially ordered space ： ウィキペディア英語版 Partially ordered space In mathematics, a partially ordered space (or pospace) is a topological space $X$ equipped with a closed partial order $\backslash leq$, i.e. a partial order whose graph $\backslash$ is a closed subset of $X^2$. From pospaces, one can define dimaps, i.e. continuous maps between pospaces which preserve the order relation. ==Equivalences== For a topological space $X$ equipped with a partial order $\backslash leq$, the following are equivalent: * $X$ is a partially ordered space. * For all $x,y\backslash in\; X$ with $x\; \backslash not\backslash leq\; y$, there are open sets $U,V\backslash subset\; X$ with $x\backslash in\; U,\; y\backslash in\; V$ and $u\; \backslash not\backslash leq\; v$ for all $u\backslash in\; U,\; v\backslash in\; V$. * For all $x,y\backslash in\; X$ with $x\; \backslash not\backslash leq\; y$, there are disjoint neighbourhoods $U$ of $x$ and $V$ of $y$ such that $U$ is an upper set and $V$ is a lower set. The order topology is a special case of this definition, since a total order is also a partial order. Every pospace is a Hausdorff space. If we take equality $=$ as the partial order, this definition becomes the definition of a Hausdorff space. 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「Partially ordered space」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.