{"title":"构建无限维例子的新维理论技术","authors":"Leonard R. Rubin, R.M. Schori, John J. Walsh","doi":"10.1016/0016-660X(79)90031-X","DOIUrl":null,"url":null,"abstract":"<div><p>Dimension theory for separable metric spaces is approached using the concept of essential families (for example, the <em>n</em> pairs of opposite faces of the <em>n</em>-cube). A new theory of essential families is developed and is used to construct examples of infinite-dimensional compacta that contain no closed <em>n</em>-dimensional (<em>n</em> ⩾ 1) subsets; these constructions are conceptually much easier than previous ones. Also, the theory is used to construct easy examples of <em>n</em>-dimensional, totally disconnected spaces.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 1","pages":"Pages 93-102"},"PeriodicalIF":0.0000,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90031-X","citationCount":"51","resultStr":"{\"title\":\"New dimension-theory techniques for constructing infinite-dimensional examples\",\"authors\":\"Leonard R. Rubin, R.M. Schori, John J. Walsh\",\"doi\":\"10.1016/0016-660X(79)90031-X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Dimension theory for separable metric spaces is approached using the concept of essential families (for example, the <em>n</em> pairs of opposite faces of the <em>n</em>-cube). A new theory of essential families is developed and is used to construct examples of infinite-dimensional compacta that contain no closed <em>n</em>-dimensional (<em>n</em> ⩾ 1) subsets; these constructions are conceptually much easier than previous ones. Also, the theory is used to construct easy examples of <em>n</em>-dimensional, totally disconnected spaces.</p></div>\",\"PeriodicalId\":100574,\"journal\":{\"name\":\"General Topology and its Applications\",\"volume\":\"10 1\",\"pages\":\"Pages 93-102\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1979-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0016-660X(79)90031-X\",\"citationCount\":\"51\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Topology and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0016660X7990031X\",\"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/0016660X7990031X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
New dimension-theory techniques for constructing infinite-dimensional examples
Dimension theory for separable metric spaces is approached using the concept of essential families (for example, the n pairs of opposite faces of the n-cube). A new theory of essential families is developed and is used to construct examples of infinite-dimensional compacta that contain no closed n-dimensional (n ⩾ 1) subsets; these constructions are conceptually much easier than previous ones. Also, the theory is used to construct easy examples of n-dimensional, totally disconnected spaces.
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