{"title":"关于将连续函数扩展为可度量AE的问题","authors":"L.I. Sennott","doi":"10.1016/0016-660X(78)90002-8","DOIUrl":null,"url":null,"abstract":"<div><p>We say that a subset <em>S</em> of a topological space <em>X</em> is <em>M</em>-embedded (<em>M</em><sup><em>N<sub>0</sub></em></sup>-embedded) in <em>X</em> if every map from <em>S</em> to a (separable) metrizable AE can be extended over <em>X</em>. Characterizations of <em>M</em>-and <em>M<em><sup>N<sub>O</sub></sup></em></em>-embedding are given and we prove that <em>S</em> is <em>M</em>-embedded (<em>M</em><sup><em>N<sub>O</sub></em></sup>-embedded) in <em>X</em> iff(<em>X,S</em>) has the Homotopy Extension Property with respect to every (seperable) ANR space.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 3","pages":"Pages 219-228"},"PeriodicalIF":0.0000,"publicationDate":"1978-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90002-8","citationCount":"8","resultStr":"{\"title\":\"On extending continuous functions into a metrizable AE\",\"authors\":\"L.I. Sennott\",\"doi\":\"10.1016/0016-660X(78)90002-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We say that a subset <em>S</em> of a topological space <em>X</em> is <em>M</em>-embedded (<em>M</em><sup><em>N<sub>0</sub></em></sup>-embedded) in <em>X</em> if every map from <em>S</em> to a (separable) metrizable AE can be extended over <em>X</em>. Characterizations of <em>M</em>-and <em>M<em><sup>N<sub>O</sub></sup></em></em>-embedding are given and we prove that <em>S</em> is <em>M</em>-embedded (<em>M</em><sup><em>N<sub>O</sub></em></sup>-embedded) in <em>X</em> iff(<em>X,S</em>) has the Homotopy Extension Property with respect to every (seperable) ANR space.</p></div>\",\"PeriodicalId\":100574,\"journal\":{\"name\":\"General Topology and its Applications\",\"volume\":\"8 3\",\"pages\":\"Pages 219-228\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0016-660X(78)90002-8\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Topology and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0016660X78900028\",\"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/0016660X78900028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On extending continuous functions into a metrizable AE
We say that a subset S of a topological space X is M-embedded (MN0-embedded) in X if every map from S to a (separable) metrizable AE can be extended over X. Characterizations of M-and MNO-embedding are given and we prove that S is M-embedded (MNO-embedded) in X iff(X,S) has the Homotopy Extension Property with respect to every (seperable) ANR space.
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