We study the infimum of theHausdorff and Vietoris topologies onthe hyperspace of a metric space. Weshow that this topology coincideswith the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or is aUC space
Levi, S., Lucchetti, R., Pelant, J. (1993). On the infimum of the Hausdorff and Vietoris topologies. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 118(3), 971-978 [10.1090/S0002-9939-1993-1165059-1].
On the infimum of the Hausdorff and Vietoris topologies
LEVI, SANDRO;
1993
Abstract
We study the infimum of theHausdorff and Vietoris topologies onthe hyperspace of a metric space. Weshow that this topology coincideswith the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or is aUC space
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