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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 Disjoint union (topology) ： ウィキペディア英語版 Disjoint union (topology) In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. Roughly speaking, two or more spaces may be considered together, each looking as it would alone. The name ''coproduct'' originates from the fact that the disjoint union is the categorical dual of the product space construction. ==Definition== Let be a family of topological spaces indexed by ''I''. Let :$X\; =\; \backslash coprod\_i\; X\_i$ be the disjoint union of the underlying sets. For each ''i'' in ''I'', let :$\backslash varphi\_i\; :\; X\_i\; \backslash to\; X\backslash ,$ be the canonical injection (defined by $\backslash varphi\_i(x)=(x,i)$). The disjoint union topology on ''X'' is defined as the finest topology on ''X'' for which the canonical injections are continuous. Explicitly, the disjoint union topology can be described as follows. A subset ''U'' of ''X'' is open in ''X'' if and only if its preimage $\backslash varphi\_i^(U)$ is open in ''X''''i'' for each ''i'' ∈ ''I''. Yet another formulation is that a subset ''V'' of ''X'' is open relative to ''X'' iff its intersection with ''Xi'' is open relative to ''Xi'' for each ''i''. 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「Disjoint union (topology)」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.