We study infima of families of topologies on the hyperspace of a metrizable space. We prove that Kuratowski convergence is the infimum, in the lattice of convergences, of all Wijsman topologies and that the cocompact topology on a metric space which is complete for a metric d is the infimum of the upper Wijsman topologies arising from metrics that are uniformly equivalent to d
Costantini, C., Levi, S., Pelant, J. (1995). Infima of hyperspace topologies. MATHEMATIKA, 42(1), 67-86 [10.1112/S0025579300011360].
Infima of hyperspace topologies
Levi, S;
1995
Abstract
We study infima of families of topologies on the hyperspace of a metrizable space. We prove that Kuratowski convergence is the infimum, in the lattice of convergences, of all Wijsman topologies and that the cocompact topology on a metric space which is complete for a metric d is the infimum of the upper Wijsman topologies arising from metrics that are uniformly equivalent to d
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