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On the converse of Tietze-Urysohn's extension theorem.

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Garrido, M. Isabel and Jaramillo Aguado, Jesús Ángel (1999) On the converse of Tietze-Urysohn's extension theorem. Questions and Answers in General Topology, 17 (1). pp. 31-34. ISSN 0918-4732

Official URL: http://qagt.za.org/year1996?vol=19


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Abstract

From the text: "Problem A: Characterize (normal) spaces in which every C -embedded subset is closed. Problem B: Characterize (normal) spaces in which every C ∗ -embedded subset is closed. Our aim here is to call attention to the above problems, and provide some partial results in this line. Question C: Suppose that X and Y are completely regular spaces in which every C -embedded subset is closed. If C(X) is isomorphic to C(Y) , is then X homeomorphic to Y ? Question D: Suppose that X and Y are completely regular spaces in which every C ∗ -embedded subset is closed. If C ∗ (X) is isomorphic to C ∗ (Y) , is then X homeomorphic to Y ?''


Item Type:Article
Uncontrolled Keywords:closedness
Subjects:Sciences > Mathematics > Topology
ID Code:21694
Deposited On:05 Jun 2013 15:44
Last Modified:12 Dec 2018 15:13

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