{"title":"映射规范性的函数方法","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":"{\"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}","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}
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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