Functional approach to the normality of mappings

Mikhail Yourievich Liseev
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Abstract

In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for mappings is proven. Characterizations of the normality properties of mappings are given and the notion of a perfect normality of a mapping is introduced. It seems to be the most optimal in this approach.
映射规范性的函数方法
文章发展了使用 $f$ 连续函数(映射)及其族的技术。文章提出了乌里索定理贴图的证明,并证明了布劳威尔-蒂叶兹-乌里索扩展定理贴图的变体。给出了映射的正则性特征,并引入了映射的完全正则性概念。在这种方法中,它似乎是最优的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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