On quasi-uniformities in hyperspaces

Berthiaume, Gilles

doi:10.1090/S0002-9939-1977-0482620-9

On quasi-uniformities in hyperspaces
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by Gilles Berthiaume

Proc. Amer. Math. Soc. 66 (1977), 335-343

DOI: https://doi.org/10.1090/S0002-9939-1977-0482620-9

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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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