{"title":"Functional approach to the normality of mappings","authors":"Mikhail Yourievich Liseev","doi":"arxiv-2406.08061","DOIUrl":null,"url":null,"abstract":"In the article a technique of the usage of $f$-continuous functions (on\nmappings) and their families is developed. A proof of the Urysohn's Lemma for\nmappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension\nTheorem for mappings is proven. Characterizations of the normality properties\nof mappings are given and the notion of a perfect normality of a mapping is\nintroduced. It seems to be the most optimal in this approach.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.08061","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In the article a technique of the usage of $f$-continuous functions (on
mappings) and their families is developed. A proof of the Urysohn's Lemma for
mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension
Theorem for mappings is proven. Characterizations of the normality properties
of mappings are given and the notion of a perfect normality of a mapping is
introduced. It seems to be the most optimal in this approach.
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