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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A nonlocally connected continuum $ X$ such that $ C(X)$ is a retract of $ 2\sp{X}$


Author: Jack T. Goodykoontz
Journal: Proc. Amer. Math. Soc. 91 (1984), 319-322
MSC: Primary 54B20; Secondary 54C15, 54F20
MathSciNet review: 740194
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Abstract: Let $ X$ be a metric continuum and let $ {2^X}\left( {C\left( X \right)} \right)$ denote the hyperspace of closed subsets (subcontinua) of $ X$. An example is given of a nonlocally connected continuum $ X$ such that $ C\left( X \right)$ is a retract of $ {2^X}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740194-2
PII: S 0002-9939(1984)0740194-2
Keywords: Continuum, hyperspace, retract, smooth dendroid
Article copyright: © Copyright 1984 American Mathematical Society