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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 Sequentially compact space ： ウィキペディア英語版 Sequentially compact space In mathematics, a topological space is sequentially compact if every infinite sequence has a convergent subsequence. For general topological spaces, the notions of compactness and sequential compactness are not equivalent; they are, however, equivalent for metric spaces. A metric space X is sequentially compact if every sequence has a convergent subsequence which converges to a point in X. == Examples and properties == The space of all real numbers with the standard topology is not sequentially compact; the sequence for all natural numbers ''n'' is a sequence that has no convergent subsequence. If a space is a metric space, then it is sequentially compact if and only if it is compact.〔Willard, 17G, p. 125.〕 However in general there exist sequentially compact spaces that are not compact (such as the first uncountable ordinal with the order topology), and compact spaces that are not sequentially compact (such as the product of $2^=\backslash mathfrak\; c$ copies of the closed unit interval).〔Steen and Seebach, Example 105, pp. 125—126.〕 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「Sequentially compact 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.