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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyperspaces of cones and fans
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by Carl Eberhart and Sam B. Nadler PDF
Proc. Amer. Math. Soc. 77 (1979), 279-288 Request permission

Abstract:

In this paper we investigate the structure of the hyperspaces of subcontinua of some nonlocally connected continua. It is shown that if X is either the cone over any infinite compact metric space or a fan with an infinite number of endpoints, then the space of subcontinua containing the vertex of X is homeomorphic to the Hilbert cube. The hyperspace of subcontinua of a smooth fan (i.e., a subcontinuum of the cone over the Cantor set) is completely described. Also we discuss the question of when two “nicely embedded” copies of the Hilbert cube in a hyperspace have a Hilbert cube sum. In connection with this we describe two spaces, one decomposable and one indecomposable, whose hyperspaces of continua are homeomorphic.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 77 (1979), 279-288
  • MSC: Primary 54B20; Secondary 54F20, 54F50
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0542098-5
  • MathSciNet review: 542098