On quasi-uniformities in hyperspaces
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- by Gilles Berthiaume PDF
- Proc. Amer. Math. Soc. 66 (1977), 335-343 Request permission
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.References
-
C. Berge, Topological spaces, Oliver and Boyd, Edinburgh, 1963.
N. Bourbaki, Elements of mathematics. General topology. Part I, Addison-Wesley, Reading, Mass., 1966.
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- Norman Levine, On Pervin’s quasi uniformity, Math. J. Okayama Univ. 14 (1969/70), 97–102. MR 292020
- Norman Levine and William J. Stager Jr., On the hyperspace of a quasi-uniform space, Math. J. Okayama Univ. 15 (1971/72), 101–106. MR 322821
- Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI 10.1090/S0002-9947-1951-0042109-4
- M. G. Murdeshwar and S. A. Naimpally, Quasi-uniform topological spaces, P. Noordhoff Ltd., Groningen, 1966. MR 0211386
- William J. Pervin, Uniformization of neighborhood axioms, Math. Ann. 147 (1962), 313–315. MR 140082, DOI 10.1007/BF01440952
Additional Information
- © Copyright 1977 American Mathematical Society
- 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