On compact metric spaces and the group of Baire equivalences
E. Lorch (1968)
Studia Mathematica
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E. Lorch (1968)
Studia Mathematica
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Anna Kucia (1990)
Commentationes Mathematicae Universitatis Carolinae
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M. M. Drešević (1980)
Matematički Vesnik
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Sianesi, Francesca (1999)
Serdica Mathematical Journal
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The present paper contains results characterizing relatively compact subsets of the space of the closed subsets of a metrizable space, equipped with various hypertopologies. We investigate the hyperspace topologies that admit a representation as weak topologies generated by families of gap functionals defined on closed sets, as well as hit-and-miss topologies and proximal-hit and-miss topologies.
Lucchetti, Roberto, Pasquale, Angela (1994)
Journal of Convex Analysis
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Artur Bartoszewicz, Małgorzata Filipczak, Andrzej Kowalski, Małgorzata Terepeta (2014)
Open Mathematics
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Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.