{"title":"超空间的循环连通性定理","authors":"L.E. Ward Jr.","doi":"10.1016/0016-660X(79)90041-2","DOIUrl":null,"url":null,"abstract":"<div><p>It is proved that if <em>X</em> is a (metric) continuum, if <em>C</em>(<em>X</em>) is the space of nonempty closed connected subsets of <em>X</em> with the Hausdorff metric, and if <em>A</em><sub>1</sub>,…,<em>A</em><sub><em>n</em></sub> are members of <em>C</em>(<em>X</em>) such that each of the sets <em>C</em>(<em>X</em>)-{<em>A<sub>i</sub></em>} is arcwise connected, then <em>C</em>(<em>X</em>)-{<em>A</em><sub>1</sub>,…,<em>A<sub>n</sub></em>} is arcwise connected.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 3","pages":"Pages 291-295"},"PeriodicalIF":0.0000,"publicationDate":"1979-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90041-2","citationCount":"1","resultStr":"{\"title\":\"A cyclic connectivity theorem for hyperspaces\",\"authors\":\"L.E. Ward Jr.\",\"doi\":\"10.1016/0016-660X(79)90041-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is proved that if <em>X</em> is a (metric) continuum, if <em>C</em>(<em>X</em>) is the space of nonempty closed connected subsets of <em>X</em> with the Hausdorff metric, and if <em>A</em><sub>1</sub>,…,<em>A</em><sub><em>n</em></sub> are members of <em>C</em>(<em>X</em>) such that each of the sets <em>C</em>(<em>X</em>)-{<em>A<sub>i</sub></em>} is arcwise connected, then <em>C</em>(<em>X</em>)-{<em>A</em><sub>1</sub>,…,<em>A<sub>n</sub></em>} is arcwise connected.</p></div>\",\"PeriodicalId\":100574,\"journal\":{\"name\":\"General Topology and its Applications\",\"volume\":\"10 3\",\"pages\":\"Pages 291-295\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1979-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0016-660X(79)90041-2\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Topology and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0016660X79900412\",\"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/0016660X79900412","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is proved that if X is a (metric) continuum, if C(X) is the space of nonempty closed connected subsets of X with the Hausdorff metric, and if A1,…,An are members of C(X) such that each of the sets C(X)-{Ai} is arcwise connected, then C(X)-{A1,…,An} is arcwise connected.
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