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

On the infimum of the Hausdorff and Vietoris topologies


Authors: S. Levi, R. Lucchetti and J. Pelant
Journal: Proc. Amer. Math. Soc. 118 (1993), 971-978
MSC: Primary 54B20; Secondary 54E35
MathSciNet review: 1165059
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Abstract: We study the infimum of the Hausdorff and Vietoris topologies on the hyperspace of a metric space. We show that this topology coincides with the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or is a UC space.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1165059-1
PII: S 0002-9939(1993)1165059-1
Article copyright: © Copyright 1993 American Mathematical Society