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PROOFS OF URYSOHN’S LEMMA AND THE TIETZE EXTENSION THEOREM VIA THE CANTOR FUNCTION

Published online by Cambridge University Press:  03 July 2020

FLORICA C. CÎRSTEA*
Affiliation:
School of Mathematics and Statistics, The University of Sydney, Camperdown, NSW 2006, Australia email florica.cirstea@sydney.edu.au

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.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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