拓扑空间上的Lipschitz函数

IF 0.3 Q4 LOGIC

Journal of Logic and Analysis Pub Date : 2010-10-08 DOI:10.4115/JLA.2013.5.8

I. Yaacov

{"title":"拓扑空间上的Lipschitz函数","authors":"I. Yaacov","doi":"10.4115/JLA.2013.5.8","DOIUrl":null,"url":null,"abstract":"We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such functions with topometric versions of classical separation axioms, namely, nor- mality and complete regularity, as well as with completions of topometric spaces. We also recover a compact topometric space X from the lattice of continuous 1-Lipschitz functions on X , in analogy with the recovery of a compact topological space X from the structure of (real or complex) functions on X. 2010 Mathematics Subject Classification 54D15 (primary); 54E99, 46E05 (sec- ondary)","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"5 1","pages":"1-21"},"PeriodicalIF":0.3000,"publicationDate":"2010-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Lipschitz functions on topometric spaces\",\"authors\":\"I. Yaacov\",\"doi\":\"10.4115/JLA.2013.5.8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such functions with topometric versions of classical separation axioms, namely, nor- mality and complete regularity, as well as with completions of topometric spaces. We also recover a compact topometric space X from the lattice of continuous 1-Lipschitz functions on X , in analogy with the recovery of a compact topological space X from the structure of (real or complex) functions on X. 2010 Mathematics Subject Classification 54D15 (primary); 54E99, 46E05 (sec- ondary)\",\"PeriodicalId\":53872,\"journal\":{\"name\":\"Journal of Logic and Analysis\",\"volume\":\"5 1\",\"pages\":\"1-21\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2010-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Logic and Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4115/JLA.2013.5.8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic and Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4115/JLA.2013.5.8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}

引用次数: 3

摘要

我们研究了拓扑空间上的(度量上的)Lipschitz函数和(拓扑上的)连续函数，并在经典拓扑中使用普通连续函数的情况下使用它们。我们研究了这类函数与经典分离公理的拓扑版本，即非不规则性和完全正则性，以及拓扑空间的完备性的关系。我们也从X上的连续1-Lipschitz函数的晶格中恢复紧致拓扑空间X，类似于从X上的(实数或复数)函数的结构中恢复紧致拓扑空间X。54E99, 46E05(二级)

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Lipschitz functions on topometric spaces

We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such functions with topometric versions of classical separation axioms, namely, nor- mality and complete regularity, as well as with completions of topometric spaces. We also recover a compact topometric space X from the lattice of continuous 1-Lipschitz functions on X , in analogy with the recovery of a compact topological space X from the structure of (real or complex) functions on X. 2010 Mathematics Subject Classification 54D15 (primary); 54E99, 46E05 (sec- ondary)

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Logic and Analysis LOGIC-

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

35 weeks

期刊介绍： "Journal of Logic and Analysis" publishes papers of high quality involving interaction between ideas or techniques from mathematical logic and other areas of mathematics (especially - but not limited to - pure and applied analysis). The journal welcomes papers in nonstandard analysis and related areas of applied model theory; papers involving interplay between mathematics and logic (including foundational aspects of such interplay); mathematical papers using or developing analytical methods having connections to any area of mathematical logic. "Journal of Logic and Analysis" is intended to be a natural home for papers with an essential interaction between mathematical logic and other areas of mathematics, rather than for papers purely in logic or analysis.