{"title":"THE BAIRE CATEGORY OF THE HYPERSPACE OF NONTRIVIAL CONVERGENT SEQUENCES","authors":"M. Poplawski","doi":"10.2478/9788366675360-018","DOIUrl":null,"url":null,"abstract":"Assume that $X$ is a regular space. We study topological properties of the family $S_c(X)$ of nontrivial convergent sequences in $X$ equipped with the Vietoris topology. We show that if $X$ has no isolated points, then $S_c(X)$ is a space of the first category which answers the question posed by S. Garcia-Ferreira and Y.F. Ortiz-Castillo.","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"123 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/9788366675360-018","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
Assume that $X$ is a regular space. We study topological properties of the family $S_c(X)$ of nontrivial convergent sequences in $X$ equipped with the Vietoris topology. We show that if $X$ has no isolated points, then $S_c(X)$ is a space of the first category which answers the question posed by S. Garcia-Ferreira and Y.F. Ortiz-Castillo.
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