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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 cylinder set ： ウィキペディア英語版 cylinder set In mathematics, a cylinder set is the natural open set of a product topology. Cylinder sets are particularly useful in providing the base of the natural topology of the product of a countable number of copies of a set. If ''V'' is a finite set, then each element of ''V'' can be represented by a letter, and the countable product can be represented by the collection of strings of letters. ==General definition== Consider the cartesian product $\backslash textstyle\; X\; =\; \backslash prod\_\; X\_\backslash ,$ of topological spaces $X\_\backslash alpha$, indexed by some index $\backslash alpha$. The canonical projection is the function $p\_\; :\; X\; \backslash to\; X\_$ that maps every element of the product to its $\backslash alpha$ component. Then, given any open set $U\backslash subset\; X\_\backslash alpha$, the preimage $p\_\backslash alpha^(U)$ is called an open cylinder. The intersection of a finite number of open cylinders is a cylinder set. The collection of open cylinders form a subbase of the product topology on $X$; the collection of all cylinder sets thus form a basis. The restriction that the cylinder set be the intersection of a finite number of open cylinders is important; allowing infinite intersections generally results in a finer topology. In this case, the resulting topology is the box topology; cylinder sets are never Hilbert cubes. 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「cylinder set」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.