MAPPINGS WITH THE SECOND COUNTABILITY AXIOM

Authors

  • К. Ishmakhametov Kyrgyz-Russian Slavic University named after B. Yeltsin Author

Keywords:

topological mapping, second axiom of countability, final compactness, regularity, normality of mapping, network

Abstract

This article examines the topological properties of continuous mappings, which are subject to fundamental concepts in space theory, such as networks, bases, and the countability axioms. The author proves that mappings with the second countability axiom possess the Lindelöf property and are finally compact. The main result of the paper is a proof that a regular, finally compact mapping is normal, which generalizes the classical theorems of Tikhonov and Vedenisov.

References

1. Б.А. Пасынков. О распространении на отображения некоторых понятий и утверждений, касающихся пространств. Отображения и функторы. Сборник. Москва, Изд-во МГУ, 1984.

2. П.С. Александров, Б.А. Пасынков. Введение в теорию размеренности. Изд. «Наука», Москва, 1973.

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Published

2026-06-05

Issue

Vol. 19 No. 1 (2014): СОВРЕМЕННЫЕ ПРОБЛЕМЫ МЕХАНИКИ СПЛОШНЫХ СРЕД

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