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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 Hilbert cube ： ウィキペディア英語版 Hilbert cube In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore, many interesting topological spaces can be embedded in the Hilbert cube; that is, can be viewed as subspaces of the Hilbert cube (see below). ==Definition== The Hilbert cube is best defined as the topological product of the intervals () for ''n'' = 1, 2, 3, 4, ... That is, it is a cuboid of countably infinite dimension, where the lengths of the edges in each orthogonal direction form the sequence $\backslash lbrace\; 1/n\; \backslash rbrace\_\{n\backslash in\backslash mathbb\{N\}\}$. The Hilbert cube is homeomorphic to the product of countably infinitely many copies of the unit interval (). In other words, it is topologically indistinguishable from the unit cube of countably infinite dimension. If a point in the Hilbert cube is specified by a sequence $\backslash lbrace\; a\_n\; \backslash rbrace$ with $0\; \backslash leq\; a\_n\; \backslash leq\; 1/n$, then a homeomorphism to the infinite dimensional unit cube is given by $h(a)\_n\; =\; n\backslash cdot\; a\_n$. 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「Hilbert cube」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.