On the infimum of the Hausdorff and Vietoris topologies

Levi, S.; Lucchetti, R.; Pelant, J.

doi:10.1090/S0002-9939-1993-1165059-1

On the infimum of the Hausdorff and Vietoris topologies
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by S. Levi, R. Lucchetti and J. Pelant PDF

Proc. Amer. Math. Soc. 118 (1993), 971-978 Request permission

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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