{"title":"自由Banach空间与Lipschitz映射的扩展","authors":"M. Dubei , E.D. Tymchatyn , A. Zagorodnyuk","doi":"10.1016/j.top.2009.11.020","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span><math><mi>X</mi></math></span> be a metric space. We study the free Banach space <span><math><mi>B</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> over <span><math><mi>X</mi></math></span>, that is a predual space of the Banach space of all Lipschitz functions on <span><math><mi>X</mi></math></span> which preserve a marked point <span><math><mi>θ</mi><mo>∈</mo><mi>X</mi></math></span>. Some applications to the extension theory of Lipschitz and two-Lipschitz functions are obtained.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"48 2","pages":"Pages 203-212"},"PeriodicalIF":0.0000,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2009.11.020","citationCount":"8","resultStr":"{\"title\":\"Free Banach spaces and extension of Lipschitz maps\",\"authors\":\"M. Dubei , E.D. Tymchatyn , A. Zagorodnyuk\",\"doi\":\"10.1016/j.top.2009.11.020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span><math><mi>X</mi></math></span> be a metric space. We study the free Banach space <span><math><mi>B</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> over <span><math><mi>X</mi></math></span>, that is a predual space of the Banach space of all Lipschitz functions on <span><math><mi>X</mi></math></span> which preserve a marked point <span><math><mi>θ</mi><mo>∈</mo><mi>X</mi></math></span>. Some applications to the extension theory of Lipschitz and two-Lipschitz functions are obtained.</p></div>\",\"PeriodicalId\":54424,\"journal\":{\"name\":\"Topology\",\"volume\":\"48 2\",\"pages\":\"Pages 203-212\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.top.2009.11.020\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040938309000329\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938309000329","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Free Banach spaces and extension of Lipschitz maps
Let be a metric space. We study the free Banach space over , that is a predual space of the Banach space of all Lipschitz functions on which preserve a marked point . Some applications to the extension theory of Lipschitz and two-Lipschitz functions are obtained.
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