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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 Kline sphere characterization ： ウィキペディア英語版 Kline sphere characterization In mathematics, a Kline sphere characterization, named after John Robert Kline, is a topological characterization of a two-dimensional sphere in terms of what sort of subset separates it. Its proof was one of the first notable accomplishments of R. H. Bing; Bing gave an alternate proof using brick partitioning in his paper ''Complementary domains of continuous curves'' 〔Bing, R.H., Complementary domains of continuous curves, ''Fund. Math.'' 36 (1949), (303-318 ).〕 A simple closed curve in a two-dimensional sphere (for instance, its equator) separates the sphere into two pieces upon removal. If one removes a pair of points from a sphere, however, the remainder is connected. Kline's sphere characterization states that the converse is true: If a nondegenerate locally connected metric continuum is separated by any simple closed curve but by no pair of points, then it is a two-dimensional sphere. ==References== *Bing, R. H., The Kline sphere characterization problem, ''Bulletin of the American Mathematical Society'' 52 (1946), (644–653 ). 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「Kline sphere characterization」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.