{"title":"可度量空间的自由拓扑群","authors":"V. Uspenskiĭ","doi":"10.1070/IM1991V037N03ABEH002163","DOIUrl":null,"url":null,"abstract":"The free topological group F(X) of an arbitrary metrizable space X is complete in the Weil sense. If Y is a closed subspace of a metrizable space X, then F(Y) is a topological subgroup of F(X).","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"75 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"89","resultStr":"{\"title\":\"FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES\",\"authors\":\"V. Uspenskiĭ\",\"doi\":\"10.1070/IM1991V037N03ABEH002163\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The free topological group F(X) of an arbitrary metrizable space X is complete in the Weil sense. If Y is a closed subspace of a metrizable space X, then F(Y) is a topological subgroup of F(X).\",\"PeriodicalId\":159459,\"journal\":{\"name\":\"Mathematics of The Ussr-izvestiya\",\"volume\":\"75 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"89\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1991V037N03ABEH002163\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1991V037N03ABEH002163","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The free topological group F(X) of an arbitrary metrizable space X is complete in the Weil sense. If Y is a closed subspace of a metrizable space X, then F(Y) is a topological subgroup of F(X).
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