Pub Date : 2018-01-17DOI: 10.2478/9788366675360-018
M. Poplawski
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.
{"title":"THE BAIRE CATEGORY OF THE HYPERSPACE OF NONTRIVIAL CONVERGENT SEQUENCES","authors":"M. Poplawski","doi":"10.2478/9788366675360-018","DOIUrl":"https://doi.org/10.2478/9788366675360-018","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":0.0,"publicationDate":"2018-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127428490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-04-01DOI: 10.2478/9788366675360-002
T. Banakh
{"title":"A POLISH GROUP CONTAINING A HAAR NULL Fα-SUBGROUP THAT CANNOT BE ENLARGED TO A HAAR NULL Gδ-SET","authors":"T. Banakh","doi":"10.2478/9788366675360-002","DOIUrl":"https://doi.org/10.2478/9788366675360-002","url":null,"abstract":"","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126729273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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