{"title":"关于arhangel' skiy的一个定理的注解","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":"{\"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}","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}
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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