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Proceedings of the American Mathematical Society

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

 

 

$ C(X)$ is not necessarily a retract of $ 2\sp{X}$


Author: Jack T. Goodykoontz
Journal: Proc. Amer. Math. Soc. 67 (1977), 177-178
MSC: Primary 54F15; Secondary 54B20
DOI: https://doi.org/10.1090/S0002-9939-1977-0458377-4
MathSciNet review: 0458377
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Abstract: Let X be a continuum and $ {2^X}(C(X))$ denote the hyperspace of closed subsets (subcontinua) of X. An example is given of a continuum X such that $ C(X)$ is not a retract of $ {2^X}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0458377-4
Keywords: Continuum, hyperspace, retract
Article copyright: © Copyright 1977 American Mathematical Society