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Proceedings of the American Mathematical Society

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

 

 

On quasi-uniformities in hyperspaces


Author: Gilles Berthiaume
Journal: Proc. Amer. Math. Soc. 66 (1977), 335-343
MSC: Primary 54B20; Secondary 54E15
DOI: https://doi.org/10.1090/S0002-9939-1977-0482620-9
MathSciNet review: 0482620
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Abstract: Quasi-uniformities in spaces of subsets are investigated. It is shown, by means of examples, how quasi-uniformities can play a unifying role in the study of topological structures in hyperspaces. The main application is the following result: an infinite product of upper semicontinuous multi-valued mappings, with compact sets as values, is again upper semi-continuous.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0482620-9
Keywords: Hyperspace, quasi-uniformity, multi-valued mapping
Article copyright: © Copyright 1977 American Mathematical Society