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The Cone = Hyperspace Property

Published online by Cambridge University Press:  20 November 2018

James T. Rogers Jr.
James T. Rogers Jr.*
Affiliation:
Tulane University, New Orleans, Louisiana
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The author has recently shown [11] that the hyperspace of subcontinua of a solenoid is homeomorphic to the cone over that solenoid. This is an interesting result, for it is the first time that the hyperspace of subcontinua of a complicated space has been recognized. This homeomorphism, moreover, is the expected map; it maps the singletons onto the base of the cone and the point corresponding to the whole space onto the vertex of the cone. We say that spaces for which such natural homeomorphisms exist have the cone = hyperspace property. In the first section we prove the following theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 2 , April 1972 , pp. 279 - 285
Copyright
Copyright © Canadian Mathematical Society 1972

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