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Proceedings of the American Mathematical Society

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



A fixed point theorem for hyperspaces of $ \lambda $ connected continua

Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 53 (1975), 231-234
MSC: Primary 54F20; Secondary 54B20
Addendum: Proc. Amer. Math. Soc. 62 (1977), 374-375.
MathSciNet review: 0377828
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Abstract: Suppose that the hyperspace of compact connected subsets $ \mathcal{C}(X)$ of a $ \lambda $ connected continuum $ X$ can be $ \epsilon $-mapped (for each $ \epsilon > 0$) into the plane. We prove that $ X$ is either arc-like or circle-like. It follows from this theorem and results of J. T. Rogers, Jr. and J. Segal that $ \mathcal{C}(X)$ has the fixed point property.

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Keywords: Hyperspaces, chainable continua, arc-like continua, circle-like continua, fixed point property, lambda connectivity, hereditarily decomposable continua, disk-like continua, triod, snake-like continua, unicoherence, $ \epsilon $-map into the plane, antipodal points, Borsuk-Ulam theorem
Article copyright: © Copyright 1975 American Mathematical Society

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