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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 metrization theorem ： ウィキペディア英語版 metrization theorem In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space $(X,\backslash tau)$ is said to be metrizable if there is a metric :$d\backslash colon\; X\; \backslash times\; X\; \backslash to\; [0,\backslash infty)$ such that the topology induced by ''d'' is $\backslash tau$. Metrization theorems are theorems that give sufficient conditions for a topological space to be metrizable. ==Properties== Metrizable spaces inherit all topological properties from metric spaces. For example, they are Hausdorff paracompact spaces (and hence normal and Tychonoff) and first-countable. However, some properties of the metric, such as completeness, cannot be said to be inherited. This is also true of other structures linked to the metric. A metrizable uniform space, for example, may have a different set of contraction maps than a metric space to which it is homeomorphic. 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「metrization theorem」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.