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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 continuum having its hyperspaces not locally contractible at the top


Author: Alejandro Illanes
Journal: Proc. Amer. Math. Soc. 111 (1991), 1177-1182
MSC: Primary 54B20; Secondary 54F15
MathSciNet review: 1037209
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Abstract: For a continuum $ X$, let $ C(X)$ (resp. $ {2^x}$) be the spaces of all nonempty subcontinua (resp. closed subsets) of $ X$. In this paper we answer a question of Dilks by showing an example of a continuum $ X$ such that if $ H = C(X){\text{ or }}{2^x}$, then $ H$ does not have nonempty open subsets which are contractible in $ H$. In particular, $ H$ is not locally contractible at any of its points.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1037209-7
PII: S 0002-9939(1991)1037209-7
Keywords: Hyperspaces, contractibility
Article copyright: © Copyright 1991 American Mathematical Society