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On a topologically uniformly continuous map
https://doi.org/10.26907/0021-3446-2025-10-44-49
Abstract
Let X and Y be metrizable spaces. A map X —> Y is called topologically uniformly continuous, if for every admissible metric р on X there is an admissible metric a on Y such that for the metric spaces (X, p) and (Y, a) the map (X, p) —^ (Y, a) is uniformly continuous. In this article such maps are investigated. As the main result, it is shown that, in a certain sense, topologically uniformly continuous maps are close to perfect maps.
About the Author
A. S. Bedritskiy
Belarusian State University
Belarus
Belarus
Alexander S. Bedritskiy
4 Nezavisimosti Ave., Minsk, 220030
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Review
For citations:
Bedritskiy A.S. On a topologically uniformly continuous map. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(10):44-49. (In Russ.) https://doi.org/10.26907/0021-3446-2025-10-44-49
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