{"title":"使用招收的可数紧度完全空间中的l空间","authors":"John Ginsburg","doi":"10.1016/0016-660X(78)90038-7","DOIUrl":null,"url":null,"abstract":"<div><p>The set theoretic principle ♢ is used to construct hereditarily Lindelof, non-separable subspaces of given complete spaces of countable tightness. The construction is patterned after R. B. Jensen's original use of ♢ to construct a Souslin line, and yields the following result: Suppose <em>X</em> is a regular space of countable tightness having weight at most <em>c</em>. If no non-empty <em>G</em><sub>δ</sub> set in <em>X</em> is contained in a separable subspace of <em>X</em>, and if either <em>X</em> is countably complete or has all closed subsets Baire, then <em>X</em> contains an L-space.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 1","pages":"Pages 9-17"},"PeriodicalIF":0.0000,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90038-7","citationCount":"0","resultStr":"{\"title\":\"L-spaces in complete spaces of countable tightness using ♢\",\"authors\":\"John Ginsburg\",\"doi\":\"10.1016/0016-660X(78)90038-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The set theoretic principle ♢ is used to construct hereditarily Lindelof, non-separable subspaces of given complete spaces of countable tightness. The construction is patterned after R. B. Jensen's original use of ♢ to construct a Souslin line, and yields the following result: Suppose <em>X</em> is a regular space of countable tightness having weight at most <em>c</em>. If no non-empty <em>G</em><sub>δ</sub> set in <em>X</em> is contained in a separable subspace of <em>X</em>, and if either <em>X</em> is countably complete or has all closed subsets Baire, then <em>X</em> contains an L-space.</p></div>\",\"PeriodicalId\":100574,\"journal\":{\"name\":\"General Topology and its Applications\",\"volume\":\"9 1\",\"pages\":\"Pages 9-17\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0016-660X(78)90038-7\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Topology and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0016660X78900387\",\"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/0016660X78900387","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
使用集合论原理来构造给定紧度完备空间的遗传Lindelof不可分子空间。该构造是在R. B. Jensen最初使用招收构造一条苏斯林线之后进行的，并得到以下结果:假设X是一个权值不超过c的可数紧度正则空间。如果X中的非空Gδ集合不包含在X的可分子空间中，并且如果X是可数完备的或有所有闭子集Baire，则X包含一个l空间。
L-spaces in complete spaces of countable tightness using ♢
The set theoretic principle ♢ is used to construct hereditarily Lindelof, non-separable subspaces of given complete spaces of countable tightness. The construction is patterned after R. B. Jensen's original use of ♢ to construct a Souslin line, and yields the following result: Suppose X is a regular space of countable tightness having weight at most c. If no non-empty Gδ set in X is contained in a separable subspace of X, and if either X is countably complete or has all closed subsets Baire, then X contains an L-space.
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