翻訳と辞書 Words near each other ・ Induction regulator ・ Induction sealing ・ Induction shrink fitting ・ Induction training ・ Induction variable ・ Induction welding ・ Induction-recursion (type theory) ・ Inductionism ・ Inductive amplifier ・ Inductive Automation ・ Inductive bias ・ Inductive charging ・ Inductive cleavage ・ Inductive coupling ・ Inductive data type ・ Inductive dimension ・ Inductive discharge ignition ・ Inductive effect ・ Inductive functional programming ・ Inductive logic programming ・ Inductive output tube ・ Inductive probability ・ Inductive programming ・ Inductive pump ・ Inductive reasoning ・ Inductive reasoning aptitude ・ Inductive sensor ・ Inductive set ・ Inductive transfer ・ Inductive type 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 Inductive dimension ： ウィキペディア英語版 Inductive dimension In the mathematical field of topology, the inductive dimension of a topological space ''X'' is either of two values, the small inductive dimension ind(''X'') or the large inductive dimension Ind(''X''). These are based on the observation that, in ''n''-dimensional Euclidean space ''R''''n'', (''n'' − 1)-dimensional spheres (that is, the boundaries of ''n''-dimensional balls) have dimension ''n'' − 1. Therefore it should be possible to define the dimension of a space inductively in terms of the dimensions of the boundaries of suitable open sets. The small and large inductive dimensions are two of the three most usual ways of capturing the notion of "dimension" for a topological space, in a way that depends only on the topology (and not, say, on the properties of a metric space). The other is the Lebesgue covering dimension. The term "topological dimension" is ordinarily understood to refer to Lebesgue covering dimension. For "sufficiently nice" spaces, the three measures of dimension are equal. ==Formal definition== We want the dimension of a point to be 0, and a point has empty boundary, so we start with :$\backslash operatorname(\backslash varnothing)=\backslash operatorname(\backslash varnothing)=-1$ Then inductively, ind(''X'') is the smallest ''n'' such that, for every ''$x\; \backslash isin\; X$'' and every open set ''U'' containing ''x'', there is an open ''V'' containing ''x'', where the closure of ''V'' is a subset of ''U'', such that the boundary of ''V'' has small inductive dimension less than or equal to ''n'' − 1. (In the case above, where ''X'' is Euclidean ''n''-dimensional space, ''V'' will be chosen to be an ''n''-dimensional ball centered at ''x''.) For the large inductive dimension, we restrict the choice of ''V'' still further; Ind(''X'') is the smallest ''n'' such that, for every closed subset ''F'' of every open subset ''U'' of ''X'', there is an open ''V'' in between (that is, ''F'' is a subset of ''V'' and the closure of ''V'' is a subset of ''U''), such that the boundary of ''V'' has large inductive dimension less than or equal to ''n'' − 1. 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「Inductive dimension」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.