Proofs of Urysohn's Lemma and the Tietze Extension Theorem via the Cantor function

TL;DR

This paper presents alternative proofs of Urysohn's Lemma and the Tietze Extension Theorem for normal spaces using the Cantor function, highlighting a novel approach in topology.

Contribution

It introduces a new method employing the Cantor function to prove fundamental theorems in topology, offering alternative proofs.

Findings

Proofs are simplified using the Cantor function

The approach provides new insights into normal spaces

Potential for extending methods to other topological results

Abstract

Urysohn's Lemma is a crucial property of normal spaces that deals with separation of closed sets by continuous functions. It is also a fundamental ingredient in proving the Tietze Extension Theorem, another property of normal spaces that deals with the existence of extensions of continuous functions. Using the Cantor function, we give alternative proofs for Urysohn's Lemma and the Tietze Extension Theorem.