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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 LF-space ： ウィキペディア英語版 LF-space In mathematics, an ''LF''-space is a topological vector space ''V'' that is a locally convex inductive limit of a countable inductive system $(V\_n,\; i\_)$ of Fréchet spaces. This means that ''V'' is a direct limit of the system $(V\_n,\; i\_)$ in the category of locally convex topological vector spaces and each $V\_n$ is a Fréchet space. Some authors restrict the term ''LF''-space to mean that ''V'' is a strict locally convex inductive limit, which means that the topology induced on $V\_n$ by $V\_$ is identical to the original topology on $V\_n$. The topology on ''V'' can be described by specifying that an absolutely convex subset ''U'' is a neighborhood of 0 if and only if $U\; \backslash cap\; V\_n$ is an absolutely convex neighborhood of 0 in $V\_n$ for every n. ==Properties== An ''LF''-space is barrelled and bornological (and thus ultrabornological). 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「LF-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.