翻訳と辞書 Words near each other ・ Weak noun ・ Weak NP-completeness ・ Weak ontology ・ Weak ontology (political concept) ・ Weak operator topology ・ Weak ordering ・ Weak position (poetry) ・ Weak reference ・ Weak salt ・ Weak Selection ・ Weak sister ・ Weak solution ・ Weak Spot ・ Weak symbol ・ Weak topology ・ Weak topology (polar topology) ・ Weak trace-class operator ・ Weak two bid ・ Weak value ・ Weak verb ・ Weak-Link Approach ・ Weak-star topology ・ Weak13 ・ Weakened weak form ・ Weakest Link ・ Weakest Link (Hong Kong) ・ Weakest Link (U.S. game show) ・ Weakfish ・ Weakless Universe ・ Weakley Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Weak topology (polar topology) ： ウィキペディア英語版 Weak topology (polar topology) In functional analysis and related areas of mathematics the weak topology is the coarsest polar topology, the topology with the fewest open sets, on a dual pair. The finest polar topology is called strong topology. Under the weak topology the bounded sets coincide with the relatively compact sets which leads to the important Bourbaki–Alaoglu theorem. ==Definition== Given a dual pair $(X,Y,\backslash langle\; ,\; \backslash rangle)$ the weak topology $\backslash sigma(X,Y)$ is the weakest polar topology on $X$ so that : $(X,\backslash sigma(X,Y))\text{'}\; \backslash simeq\; Y$. That is the continuous dual of $(X,\backslash sigma(X,Y))$ is equal to $Y$ up to isomorphism. The weak topology is constructed as follows: For every $y$ in $Y$ on $X$ we define a semi norm on $X$ :$p\_y:X\; \backslash to\; \backslash mathbb$ with :$p\_y(x)\; :=\; \backslash vert\; \backslash langle\; x\; ,\; y\; \backslash rangle\; \backslash vert\; \backslash qquad\; x\; \backslash in\; X$ This family of semi norms defines a locally convex topology on $X$. 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「Weak topology (polar 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.