翻訳と辞書 Words near each other ・ Universal Soil Loss Equation ・ Universal Soldier ・ Universal Soldier (1967 Donovan album) ・ Universal Soldier (1971 film) ・ Universal Soldier (1992 film) ・ Universal Soldier (franchise) ・ Universal Soldier (Pastor Troy album) ・ Universal Soldier (song) ・ Universal Soldiers ・ Universal solvent ・ Universal Sompo General Insurance Company ・ Universal Soul ・ Universal Space ・ Universal space ・ Universal space (disambiguation) ・ Universal space (topology) ・ Universal Space Interface Standard ・ Universal Space Network ・ Universal Sport Exhibition (1949) ・ Universal Sports Network ・ Universal Sports Palace Molot ・ Universal Stars ・ Universal state ・ Universal Statuary Corp. ・ Universal Storage Media ・ Universal Storage Platform ・ Universal stress protein ・ Universal Studios ・ Universal Studios Dubailand ・ Universal Studios Florida 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 Universal space (topology) ： ウィキペディア英語版 Universal space (topology) In mathematics, a universal space is a certain metric space that contains all metric spaces whose dimension is bounded by some fixed constant. A similar definition exists in topological dynamics. ==Definition== Given a class $\backslash textstyle\; \backslash mathcal$ of topological spaces, $\backslash textstyle\; \backslash mathbb\backslash in\backslash mathcal$ is universal for $\backslash textstyle\; \backslash mathcal$ if each member of $\backslash textstyle\; \backslash mathcal$ embeds in $\backslash textstyle\; \backslash mathbb$. Menger stated and proved the case $\backslash textstyle\; d=1$ of the following theorem. The theorem in full generality was proven by Nöbeling. Theorem: The $\backslash textstyle\; (2d+1)$-dimensional cube $\backslash textstyle\; ()^$ is universal for the class of compact metric spaces whose Lebesgue covering dimension is less than $\backslash textstyle\; d$. Nöbeling went further and proved: Theorem: The subspace of $\backslash textstyle\; ()^$ consisting of set of points, at most $\backslash textstyle\; d$ of whose coordinates are rational, is universal for the class of separable metric spaces whose Lebesgue covering dimension is less than $\backslash textstyle\; d$. The last theorem was generalized by Lipscomb to the class of metric spaces of (weight ) $\backslash textstyle\; \backslash alpha$, $\backslash textstyle\; \backslash alpha>\backslash aleph\_$: There exist a one-dimensional metric space $\backslash textstyle\; J\_$ such that the subspace of $\backslash textstyle\; J\_^$ consisting of set of points, at most $\backslash textstyle\; d$ of whose coordinates are "rational"'' (suitably defined), ''is universal for the class of metric spaces whose Lebesgue covering dimension is less than $\backslash textstyle\; d$ and whose weight is less than $\backslash textstyle\; \backslash alpha$. 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「Universal space (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.