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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 Tychonoff cube ： ウィキペディア英語版 Tychonoff cube In mathematics, more specifically in general topology, the Tychonoff cube is the generalization of the unit cube from the product of a finite number of unit intervals to the product of an infinite, even uncountable number of unit intervals. The Tychonoff cube is named after Andrey Tychonoff, who first considered the arbitrary product of topological spaces and who proved in the 1930s that the Tychonoff cube is compact. Tychonoff later generalized this to the product of collections of arbitrary compact spaces. This result is now known as Tychonoff's theorem and is considered one of the most important results in general topology. == Definition == Let $I$ denote the unit interval $()$. Given a cardinal number $\backslash kappa\; \backslash geq\; \backslash omega$, we define a Tychonoff cube of weight $\backslash kappa$ as the space $I^\backslash kappa$ with the product topology, i.e. the product $\backslash prod\_\; I\_s$ where $\backslash kappa$ is the cardinality of $S$ and, for all $s\backslash in\; S$, $I\_s\; =\; I$. The Hilbert cube, $I^\backslash omega$, is a special case of a Tychonoff cube. 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「Tychonoff 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.