## Hyperspaces of cones and fans

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- by Carl Eberhart and Sam B. Nadler
- Proc. Amer. Math. Soc.
**77**(1979), 279-288 - DOI: https://doi.org/10.1090/S0002-9939-1979-0542098-5
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## 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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## Bibliographic 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