Functional approach to the normality of mappings
Mikhail Yourievich Liseev
TL;DR
This paper develops a functional approach to the normality of mappings, proving key theorems like Urysohn's Lemma and the Extension Theorem for mappings, and introduces the concept of perfect normality.
Contribution
It introduces a novel functional technique for analyzing the normality of mappings and establishes new theorems and characterizations in this framework.
Findings
Proof of Urysohn's Lemma for mappings
Extension theorem for mappings analogous to Brouwer-Tietze-Urysohn
Introduction of perfect normality for mappings
Abstract
In the article a technique of the usage of -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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Functional Equations Stability Results