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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 Dimensional operator ： ウィキペディア英語版 Dimensional operator In mathematics, specifically set theory, a dimensional operator on a set ''E'' is a function from the subsets of ''E'' to the subsets of ''E''. ==Definition== If the power set of ''E'' is denoted ''P''(''E'') then a dimensional operator on ''E'' is a map :$d:P(E)\backslash rightarrow\; P(E)\backslash ,$ that satisfies the following properties for ''S'',''T'' ∈ ''P''(''E''): # ''S'' ⊆ ''d''(''S''); # ''d''(''S'') = ''d''(''d''(''S'')) (''d'' is idempotent); # if ''S'' ⊆ ''T'' then ''d''(''S'') ⊆ ''d''(''T''); # if Ω is the set of finite subsets of ''S'' then ''d''(''S'') = ∪''A''∈Ω''d''(''A''); # if ''x'' ∈ ''E'' and ''y'' ∈ ''d''(''S'' ∪ ) \ ''d''(''S''), then ''x'' ∈ ''d''(''S'' ∪ ). The final property is known as the exchange axiom.〔Julio R. Bastida, ''Field Extensions and Galois Theory'', Addison-Wesley Publishing Company, 1984, pp. 212–213.〕 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「Dimensional 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.