翻訳と辞書 Words near each other ・ Subsonic (media server) ・ SubSonic (software) ・ Subsonic aircraft ・ Subsonic ammunition ・ Subsonic and transonic wind tunnel ・ Subsonic Factor ・ Subsonic Music Festival ・ Subsonica ・ Subsource ・ Subspace ・ SubSpace (video game) ・ Subspace Encounter ・ Subspace Explorers ・ Subspace Gaussian Mixture Model ・ Subspace theorem ・ Subspace topology ・ Subspecialty ・ Subspecies ・ Subspecies (film series) ・ Subspecies of Canis lupus ・ Subspecies of Galápagos tortoise ・ Subspecific name ・ Subsporangial vesicle ・ Subsquamosal fenestra ・ SUBST ・ SubStance ・ Substance ・ Substance (Blank & Jones album) ・ Substance (Joy Division album) ・ Substance 1987 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 Subspace topology ： ウィキペディア英語版 Subspace topology In topology and related areas of mathematics, a subspace of a topological space ''X'' is a subset ''S'' of ''X'' which is equipped with a topology induced from that of ''X'' called the subspace topology (or the relative topology, or the induced topology, or the trace topology). == Definition == Given a topological space $(X,\; \backslash tau)$ and a subset $S$ of $X$, the subspace topology on $S$ is defined by :$\backslash tau\_S\; =\; \backslash lbrace\; S\; \backslash cap\; U\; \backslash mid\; U\; \backslash in\; \backslash tau\; \backslash rbrace.$ That is, a subset of $S$ is open in the subspace topology if and only if it is the intersection of $S$ with an open set in $(X,\; \backslash tau)$. If $S$ is equipped with the subspace topology then it is a topological space in its own right, and is called a subspace of $(X,\; \backslash tau)$. Subsets of topological spaces are usually assumed to be equipped with the subspace topology unless otherwise stated. Alternatively we can define the subspace topology for a subset $S$ of $X$ as the coarsest topology for which the inclusion map :$\backslash iota:\; S\; \backslash hookrightarrow\; X$ is continuous. More generally, suppose $\backslash iota$ is an injection from a set $S$ to a topological space $X$. Then the subspace topology on $S$ is defined as the coarsest topology for which $\backslash iota$ is continuous. The open sets in this topology are precisely the ones of the form $\backslash iota^(U)$ for $U$ open in $X$. $S$ is then homeomorphic to its image in $X$ (also with the subspace topology) and $\backslash iota$ is called a topological embedding. A subspace $S$ is called an open subspace if the injection $\backslash iota$ is an open map, i.e., if the forward image of an open set of $S$ is open in $X$. Likewise it is called a closed subspace if the injection $\backslash iota$ is a closed map. 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「Subspace 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.