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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 preclosure operator ： ウィキペディア英語版 preclosure operator In topology, a preclosure operator, or Čech closure operator is a map between subsets of a set, similar to a topological closure operator, except that it is not required to be idempotent. That is, a preclosure operator obeys only three of the four Kuratowski closure axioms. == Definition == A preclosure operator on a set $X$ is a map $()\_p$ :$()\_p:\backslash mathcal(X)\; \backslash to\; \backslash mathcal(X)$ where $\backslash mathcal(X)$ is the power set of $X$. The preclosure operator has to satisfy the following properties: # $()\_p\; =\; \backslash varnothing\; \backslash !$ (Preservation of nullary unions); # $A\; \backslash subseteq\; ()\_p$ (Extensivity); # $(\backslash cup\; B)\_p\; =\; ()\_p\; \backslash cup\; ()\_p$ (Preservation of binary unions). The last axiom implies the following: : 4. $A\; \backslash subseteq\; B$ implies $()\_p\; \backslash subseteq\; ()\_p$. 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「preclosure operator」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.