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

Part of: Maps and general types of spaces defined by maps Fairly general properties

Published online by Cambridge University Press:  03 July 2020

FLORICA C. CÎRSTEA Open the ORCID record for FLORICA C. CÎRSTEA [Opens in a new window]
FLORICA C. CÎRSTEA*
Affiliation:
School of Mathematics and Statistics, The University of Sydney, Camperdown, NSW 2006, Australia email florica.cirstea@sydney.edu.au
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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 lemmanormal spaceCantor set

MSC classification

Primary: 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
Secondary: 54C05: Continuous maps 54C99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 2 , April 2021 , pp. 326 - 332
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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