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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 Compact-open topology ： ウィキペディア英語版 Compact-open topology In mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces. The compact-open topology is one of the commonly used topologies on function spaces, and is applied in homotopy theory and functional analysis. It was introduced by Ralph Fox in 1945 (). == Definition == Let and be two topological spaces, and let denote the set of all continuous maps between and . Given a compact subset of and an open subset of , let denote the set of all functions such that Then the collection of all such is a subbase for the compact-open topology on . (This collection does not always form a base for a topology on .) When working in the category of compactly generated spaces, it is common to modify this definition by restricting to the subbase formed from those which are the image of a compact Hausdorff space. Of course, if is compactly generated and Hausdorff, this definition coincides with the previous one. However, the modified definition is crucial if one wants the convenient category of compactly generated weak Hausdorff spaces to be Cartesian closed, among other useful properties. The confusion between this definition and the one above is caused by differing usage of the word compact. 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「Compact-open 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.