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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク final topology ： ウィキペディア英語版 final topology In general topology and related areas of mathematics, the final topology (or strong topology or colimit topology or inductive topology) on a set $X$, with respect to a family of functions into $X$, is the finest topology on ''X'' which makes those functions continuous. The dual notion is the initial topology. == Definition == Given a set $X$ and a family of topological spaces $Y\_i$ with functions :$f\_i:\; Y\_i\; \backslash to\; X$ the final topology $\backslash tau$ on $X$ is the finest topology such that each :$f\_i:\; Y\_i\; \backslash to\; (X,\backslash tau)$ is continuous. Explicitly, the final topology may be described as follows: a subset ''U'' of ''X'' is open if and only if $f\_i^(U)$ is open in ''Y''''i'' for each ''i'' ∈ ''I''. 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「final 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.