{"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":null,"pages":null},"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\":null,\"pages\":null},\"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}
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)
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.