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Infima of hyperspace topologies
Author(s) -
Costantini C.,
Levi S.,
Pelant J.
Publication year - 1995
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300011360
Subject(s) - infimum and supremum , hyperspace , mathematics , metrization theorem , comparison of topologies , network topology , metric space , topology (electrical circuits) , weak topology (polar topology) , discrete mathematics , metric (unit) , combinatorics , pure mathematics , topological space , general topology , separable space , mathematical analysis , extension topology , computer science , operations management , economics , operating system
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 .