A new proof of Urysohn's Lemma via the Cantor function

Florica C. Cîrstea


Using the Cantor set and Cantor function, we give a new and simplified proof of Urysohn's Lemma. The latter is a crucial property of normal spaces that deals with separation of closed sets by continuous functions. Urysohn's Lemma 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.

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

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

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Tuesday, October 22, 2019