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

DOI10.1017/S000497272000057XzbMath1466.54003arXiv1910.10381WikidataQ113858147 ScholiaQ113858147MaRDI QIDQ5857600

Florica-Corina St. Cîrstea

Publication date: 1 April 2021

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.10381

zbMATH Keywords

Cantor setnormal spaceUrysohn's lemmaTietze's Extension TheoremCantor staircase function

Mathematics Subject Classification ID

Continuous maps (54C05) Singular functions, Cantor functions, functions with other special properties (26A30) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15) Maps and general types of topological spaces defined by maps (54C99)

Cites Work

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• A short proof of the Tietze-Urysohn extension theorem
• A simple proof of the Tietze-Urysohn extension theorem
• The Cantor function
• The Elements of Cantor Sets
• A Tale of Topology
• The Tietze Extension Theorem and the Open Mapping Theorem
• A "More Topological" Proof of the Tietze-Urysohn Theorem
• A Note on the History of the Cantor Set and Cantor Function
• Proofs of Urysohn's Lemma and Related Theorems by Means of Zorn's Lemma

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