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

 

Uniform convergence for a hyperspace


Author: R. J. Gazik
Journal: Proc. Amer. Math. Soc. 42 (1974), 302-306
MSC: Primary 54B20
MathSciNet review: 0331304
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Abstract: In this note a uniform convergence in the collection $ C(E)$ of nonempty, compact subsets of a separated uniform convergence space E is defined. This convergence is compared with the hyperspace convergence on $ C(E)$ and it is shown that the two convergences agree on Richardson's class $ \Gamma $. In the case of a regular $ {T_1}$ topological space (E, t) this means that there is a uniform convergence structure on E, which induces t, such that uniform convergence in $ C(E)$ is convergences in the Vietoris topology on $ C(E)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0331304-3
PII: S 0002-9939(1974)0331304-3
Keywords: Vietoris topology, uniform topology, convergence spaces, uniform convergence spaces, hyperspaces of convergence spaces
Article copyright: © Copyright 1974 American Mathematical Society