{"title":"A note on a theorem of arhangel'skiǐ","authors":"Mohammad Ismail","doi":"10.1016/0016-660X(78)90024-7","DOIUrl":null,"url":null,"abstract":"<div><p>Arhangel'skiǐ proved that the Continuum Hypothesis implies that if a regular space <em>X</em> is hereditarily of pointwise countable type then the set of points as which the character of <em>X</em> is countable is a dense subset of <em>X</em>. In this note we prove this theorem without the use of the Continuum Hypothesis.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 3","pages":"Pages 217-220"},"PeriodicalIF":0.0000,"publicationDate":"1978-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90024-7","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X78900247","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
Arhangel'skiǐ proved that the Continuum Hypothesis implies that if a regular space X is hereditarily of pointwise countable type then the set of points as which the character of X is countable is a dense subset of X. In this note we prove this theorem without the use of the Continuum Hypothesis.
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