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

Florica C. Cîrstea

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.

Keywords: Urysohn's Lemma, normal space, Cantor set.

AMS Subject Classification: Primary 54D15; secondary 54C05, 54C99.