翻訳と辞書 Words near each other ・ Pseudomonas proteolytica ・ Pseudomonas pseudoalcaligenes ・ Pseudomonas psychrophila ・ Pseudomonas psychrotolerans ・ Pseudomonas putida ・ Pseudomonas rathonis ・ Pseudomonas reptilivora ・ Pseudomonas resiniphila ・ Pseudomonas resinovorans ・ Pseudomonas rhizosphaerae ・ Pseudomonas rhodesiae ・ Pseudomonas rnk leader ・ Pseudomonas rpsL leader ・ Pseudomonas rubescens ・ Pseudometric ・ Pseudometric space ・ Pseudomiccolamia ・ Pseudomicrodes ・ Pseudomicrodon ・ Pseudomicronia ・ Pseudomigadops ・ Pseudominolia ・ Pseudominolia articulata ・ Pseudominolia biangulosa ・ Pseudominolia climacota ・ Pseudominolia gradata ・ Pseudominolia musiva ・ Pseudominolia nedyma ・ Pseudominolia splendens ・ Pseudominolia tramieri 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 Pseudometric space ： ウィキペディア英語版 Pseudometric space In mathematics, a pseudometric or semi-metric space〔Dmitri Burago, Yu D Burago, Sergei Ivanov, A Course in Metric Geometry, American Mathematical Society, 2001, ISBN 0-8218-2129-6.〕 is a generalized metric space in which the distance between two distinct points can be zero. In the same way as every normed space is a metric space, every seminormed space is a pseudometric space. Because of this analogy the term semimetric space (which has a different meaning in topology) is sometimes used as a synonym, especially in functional analysis. When a topology is generated using a family of pseudometrics, the space is called a gauge space. ==Definition== A pseudometric space $(X,d)$ is a set $X$ together with a non-negative real-valued function $d\backslash colon\; X\; \backslash times\; X\; \backslash longrightarrow\; \backslash mathbb\_$ (called a pseudometric) such that, for every $x,y,z\; \backslash in\; X$, #$d(x,y)\; \backslash geq\; 0$. #$d(x,y)\; =\; d(y,x)$ (''symmetry'') #$d(x,z)\; \backslash leq\; d(x,y)\; +\; d(y,z)$ (''subadditivity''/''triangle inequality'') Unlike a metric space, points in a pseudometric space need not be distinguishable; that is, one may have $d(x,y)=0$ for distinct values $x\backslash ne\; y$. 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「Pseudometric 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.