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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 Formal ball ： ウィキペディア英語版 Formal ball In topology, a formal ball is an extension of the notion of ball to allow negative radius. The concept of formal ball was introduced by Weihrauch and Schreiber in 1981 and the negative radius case (the generalized formal ball) by Tsuiki and Hattori in 2008. Specifically, if $(X,d)$ is a metric space and $\backslash mathbb^$ the nonnegative real numbers, then an element of $B^+(X,d)=X\backslash times\backslash mathbb^$ is a formal ball. Elements of $B(X,d)=X\backslash times\backslash mathbb$ are known as generalized formal balls. Formal balls possess a partial order $\backslash leq$ defined by $(x,r)\backslash leq(y,s)$ if $d(x,y)\backslash leq\; r-s$, identical to that defined by set inclusion. Generalized formal balls are interesting because this partial order works just as well for $B(X,d)$ as for $B^+(X,d)$, even though a generalized formal ball with negative radius does not correspond to a subset of $X$. Formal balls possess the Lawson topology and the Martin topology. ==References== K. Weihrauch and U. Schreiber 1981. "Embedding metric spaces into CPOs". ''Theoretical computer science'', 16:5-24. H. Tsuiki and Y. Hattori 2008. "Lawson topology of the space of formal balls and hyperbolic topology of a metric space". ''Theoretical computer science'', 405:198-205 Y. Hattori 2010. "Order and topological structures of posets of the formal balls on metric spaces". ''Memoirs of the Faculty of Science and Engineering. Shimane University. Series B'' 43:13-26 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「Formal ball」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.