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Continua with cones homeomorphic to hyperspaces

โœ Scribed by James T. Rogers Jr.

Book ID
103096035
Publisher
Elsevier Science
Year
1973
Weight
801 KB
Volume
3
Category
Article
ISSN
0016-660X

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โœฆ Synopsis

We investigate continua with the property that the cone ojGrer* the continuum is homeomorphic to the hyperspace of subcontinua of the cantMum. Among our results ale the following theorems: (i) Such a finite-dimensional continuum must be airiodic and onedimensional; (ii) if such a continuum is heredit-tily decomposable, then it mus: be an arc, an arl:wiseconnected circie-iike continuum, or a compactification of either [&I) or R with remainder ei,her a circle or an arc. Examples are given to show that noxne of these poAGlities may the omit ted.

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