{"title":"The regular topology on C(X, Y) revisited","authors":"A. Jindal","doi":"10.1007/s10474-024-01463-6","DOIUrl":null,"url":null,"abstract":"<div><p>This paper aims to study some important topological properties of the regular topology on <i>C</i>(<i>X</i>, <i>Y</i>), the set of all continuous functions from a Tychonoff space <i>X</i> to a metric space (<i>Y</i>, <i>d</i>). In particular, we study in detail the connectedness of the regular topology on <i>C</i>(<i>X</i>, <i>Y</i>). In the end, some important countability properties are studied.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"234 - 243"},"PeriodicalIF":0.6000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01463-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper aims to study some important topological properties of the regular topology on C(X, Y), the set of all continuous functions from a Tychonoff space X to a metric space (Y, d). In particular, we study in detail the connectedness of the regular topology on C(X, Y). In the end, some important countability properties are studied.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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