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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 Pseudo-arc ： ウィキペディア英語版 Pseudo-arc In general topology, the pseudo-arc is the simplest nondegenerate hereditarily indecomposable continuum. The pseudo-arc is an arc-like homogeneous continuum. R.H. Bing proved that, in a certain well-defined sense, most continua in R''n'', ''n'' ≥ 2, are homeomorphic to the pseudo-arc. == History == In 1920, Bronisław Knaster and Kazimierz Kuratowski asked whether a nondegenerate homogeneous continuum in the Euclidean plane R2 must be a Jordan curve. In 1921, Stefan Mazurkiewicz asked whether a nondegenerate continuum in R2 that is homeomorphic to each of its nondegenerate subcontinua must be an arc. In 1922, Knaster discovered the first example of a homogeneous hereditarily indecomposable continuum ''K'', later named the pseudo-arc, giving a negative answer to the Mazurkiewicz question. In 1948, R.H. Bing proved that Knaster's continuum is homogeneous, i.e., for any two of its points there is a homeomorphism taking one to the other. Yet also in 1948, Edwin Moise showed that Knaster's continuum is homeomorphic to each of its non-degenerate subcontinua. Due to its resemblance to the fundamental property of the arc, namely, being homeomorphic to all its nondegenerate subcontinua, Moise called his example ''M'' a pseudo-arc.〔 later showed that a ''decomposable'' continuum homeomorphic to all its nondenerate subcontinua must be an arc.〕 Bing's construction is a modification of Moise's construction of ''M'', which he had first heard described in a lecture. In 1951, Bing proved that all hereditarily indecomposable arc-like continua are homeomorphic — this implies that Knaster's ''K'', Moise's ''M'', and Bing's ''B'' are all homeomorphic. Bing also proved that the pseudo-arc is typical among the continua in a Euclidean space of dimension at least 2 or an infinite-dimensional separable Hilbert space.〔The history of the discovery of the pseudo-arc is described in , pp 228–229.〕 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「Pseudo-arc」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.