A method of working with $f$-continuous functions on mappings is developed. The method is used to derive a constructive proof of Urysohn’s Lemma for mappings. A variant of the Brouwer–Tietze–Urysohn theorem for mappings is proved. Functional characterizations are given for the normality properties of mappings. The notion of perfect normality of a mapping, which seems to be the most optimal, is introduced.
Keywords: fiberwise general topology, $f$-continuous mapping, ($\sigma$)-normal mapping, perfectly normal mapping, Urysohn’s Lemma, Brouwer–Tietze–Urysohn theorem, Vedenisov’s conditions of perfect normality
Received December 14, 2024
Revised January 13, 2025
Accepted January 17, 2025
Funding Agency: The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement no. 075-15-2019-1621.
Mikhail Yourievich Liseev, Chair of General Topology and Geometry, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119992 Russia. e-mail: liseev.mikhail@gmail.com
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Cite this article as: M.Yu. Liseev. Functional approach to the study of normality properties of mappings. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 1, pp. 119–137.
