{"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}
引用次数: 1
Abstract
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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