Neighborhoods of sphere-like continua

✍ Scribed by D. Coram; P.F. Duvall Jr.

• Book ID: 103094076
• Publisher: Elsevier Science
• Year: 1976
• Weight: 984 KB
• Volume: 6
• Category: Article
• ISSN: 0016-660X
• DOI: 10.1016/0016-660x(76)90032-5

✦ Synopsis

Let X be an Sk-like continuum iri Eu&.ean space En. It is shown that if the embedding of Xsatisfies the smailt loops con dition z nd 1 < k Q n -4, then Xhas arbitrarily small neighborhuods which are iatlmeomorphic tc SkXBnVk. It foliows that if X and 'Y are Sk-like continua in SN, 1 6; k Q n -d!., and '30th satis,fy the small loops condition, then X and Y have homeamorphii. complments if and onlg if they have the same shape.