翻訳と辞書 Words near each other ・ Particle velocity probe ・ Particle zoo ・ Particle-beam weapon ・ Particle-in-cell ・ Particle-induced X-ray emission ・ Particle-laden flows ・ Particle-size distribution ・ ParticleIllusion ・ Particles of Truth ・ Particolored flying squirrel ・ Particoloured ・ Particracy ・ Particular ・ Particular Church ・ Particular judgment ・ Particular point topology ・ Particular social group ・ Particular values of Riemann zeta function ・ Particular values of the Gamma function ・ Particularism ・ Particularly Dangerous Situation ・ Particularly vulnerable tribal group ・ Particulate (disambiguation) ・ Particulate inheritance ・ Particulate matter sampler ・ Particulate pollution ・ Particulates ・ Partido ・ Partido (Camarines Sur) ・ Partido Abe Kapampangan 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 Particular point topology ： ウィキペディア英語版 Particular point topology In mathematics, the particular point topology (or included point topology) is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. Formally, let ''X'' be any set and ''p'' ∈ ''X''. The collection :''T'' = of subsets of ''X'' is then the particular point topology on ''X''. There are a variety of cases which are individually named: * If ''X'' = we call ''X'' the Sierpiński space. This case is somewhat special and is handled separately. * If ''X'' is finite (with at least 3 points) we call the topology on ''X'' the finite particular point topology. * If ''X'' is countably infinite we call the topology on ''X'' the countable particular point topology. * If ''X'' is uncountable we call the topology on ''X'' the uncountable particular point topology. A generalization of the particular point topology is the closed extension topology. In the case when ''X'' \ has the discrete topology, the closed extension topology is the same as the particular point topology. This topology is used to provide interesting examples and counterexamples. ==Properties== ; Closed sets have empty interior : Given an open set $A\; \backslash subset\; X$ every $x\; \backslash ne\; p$ is a limit point of A. So the closure of any open set other than $\backslash emptyset$ is $X$. No closed set other than $X$ contains p so the interior of every closed set other than $X$ is $\backslash emptyset$. 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「Particular point topology」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.