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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 Generalised metric ： ウィキペディア英語版 Generalised metric In mathematics, the concept of a generalised metric is a generalisation of that of a metric, in which the distance is not a real number but taken from an arbitrary ordered field. In general, when we define metric space the distance function is taken to be a real-valued function. The real numbers form an ordered field which is Archimedean and order complete. These metric spaces have some nice properties like: in a metric space compactness, sequential compactness and countable compactness are equivalent etc. These properties may not, however, hold so easily if the distance function is taken in an arbitrary ordered field, instead of in $\backslash scriptstyle\; \backslash mathbb\; R$. ==Preliminary definition== Let be an arbitrary ordered field, and $M$ a nonempty set; a function $d\; :M\backslash times\; M\backslash to\; F^+\backslash cup\backslash$ is called a metric on $M$, iff the following conditions hold: # $d(x,y)=0\backslash Leftrightarrow\; x=y$; # $d(x,y)=d(y,x)$, commutativity; # $d(x,y)+d(y,z)\backslash le\; d(x,z)$, triangle inequality. It is not difficult to verify that the open balls $B(x,\backslash delta)\backslash ;:=\backslash$ form a basis for a suitable topology, the latter called the ''metric topology'' on $M$, with the metric in $F$. In view of the fact that $F$ in its order topology is monotonically normal, we would expect $M$ to be at least regular. 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「Generalised metric」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.