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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 Frölicher space ： ウィキペディア英語版 Frölicher space In mathematics, Frölicher spaces extend the notions of calculus and smooth manifolds. They were introduced in 1982 by the mathematician Alfred Frölicher. ==Definition== A Frölicher space consists of a non-empty set ''X'' together with a subset ''C'' of Hom(R, ''X'') called the set of smooth curves, and a subset ''F'' of Hom(''X'', R) called the set of smooth real functions, such that for each real function :''f'' : ''X'' → R in ''F'' and each curve :''c'' : R → ''X'' in ''C'', the following axioms are satisfied: # ''f'' in ''F'' if and only if for each ''γ'' in ''C'', ''f'' . ''γ'' in C∞(R, R) # ''c'' in ''C'' if and only if for each ''φ'' in ''F'', ''φ'' . ''c'' in C∞(R, R) Let ''A'' and ''B'' be two Frölicher spaces. A map :''m'' : ''A'' → ''B'' is called ''smooth'' if for each smooth curve ''c'' in ''C''''A'', ''m''.''c'' is in ''C''''B''. Furthermore the space of all such smooth maps has itself the structure of a Frölicher space. The smooth functions on '' :''C∞(''A'', ''B'') are the images of :$S\; :\; F\_B\; \backslash times\; C\_A\; \backslash times\; \backslash mathrm^(\backslash mathbf,\; \backslash mathbf)\text{'}\; \backslash to\; \backslash mathrm(\backslash mathrm^(A,\; B),\; \backslash mathbf)\; :\; (f,\; c,\; \backslash lambda)\; \backslash mapsto\; S(f,\; c,\; \backslash lambda),\; \backslash quad\; S(f,\; c,\; \backslash lambda)(m)\; :=\; \backslash lambda(f\; \backslash circ\; m\; \backslash circ\; c)$ 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「Frölicher space」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.