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On the functor properties of some hyperspace topologies
https://doi.org/10.26907/0021-3446-2025-2-15-28
Abstract
A continuous map X f→ Y and its extension expτ X f→ expτ Y are considered (expτ X is the hyperspace (endowed with a topology τ) of the topological space X, ḟ(F) = [f (F)]Y (the closure of a set f(F) in the space Y)). A necessary and sufficient condition (a modification of the Harris’ (WO) condition) of continuity of the map ḟ in the cases when τ = τLF (the locally finite topology) and τ = τF (the Fell topology) is found. When X and Y are metrizable spaces the topology τinf, as the infimum of all Hausdorff metric topologies, is considered. A sufficient condition (TUC) condition) of continuity of the map ḟ in the case when τ = τinf is found. It is also shown, that this condition is necessary, when the space Y is locally compact and second countable. The results are commented from the point of view of the category theory.
About the Authors
A. S. Bedritskiy
Belarusian State University
Belarus
Belarus
Aleksander S. Bedritskiy.
4 Nezavisimosti Ave., Minsk, 220030
V. L. Timokhovich
Belarusian State University
Belarus
Belarus
Vladimir L. Timokhovich.
4 Nezavisimosti Ave., Minsk, 220030
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Review
For citations:
Bedritskiy A.S., Timokhovich V.L. On the functor properties of some hyperspace topologies. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(2):15-28. (In Russ.) https://doi.org/10.26907/0021-3446-2025-2-15-28
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