\(T_{(\alpha,\beta)}\)-spaces and the Wallman compactification
type: Item
instance of: scholarly article
title: \(T_{(\alpha,\beta)}\)-spaces and the Wallman compactification
zbMATH Open document ID: 1072.54509
DOI: 10.1155/S0161171204404050
author: Karim Belaid
author: Othman Echi
author: Sami Lazaar
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/51691
review text: We quote the paper's summary: ``Some new separation axioms are introduced and studied. We also deal with maps having an extension to a homeomorphism between the Wallman compactifcations of their domains and ranges''. [Reviewer's remark: Unfortunately, some of the ``new'' separation axioms are well-known. For example, what the authors call \(T_{(0,1)}\)-spaces are nothing but \(R_0\)-spaces, sometimes also called symmetric spaces. They were introduced by \textit{N. A. Shanin} in [C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 38, 110--113 (1943; Zbl 0061.39607)] and rediscovered by \textit{A. S. Davis} in [Am. Math. Mon. 68, 886--894 (1961; Zbl 0106.15504)]. Since the underlying topology of nearness spaces is always \(R_0\), they are widely used. Similarly, what the authors call \(T_{(0,2)}\)-spaces are nothing but \(R_1\)-spaces in the sense of A. S. Davis. The properties used to define \(T_{(0,1)}\)-spaces (respectively \(T_{(0,2)}\)-spaces) are well-known characterizations of \(R_0\)-spaces (respectively \(R_1\)-spaces) which can be found, e.g., in [\textit{C. Dorsett}, Kyungpook Math. J. 17, 175--179 (1977; Zbl 0385.54012)]. For a comprehensive early survey on separation axioms we refer to [\textit{A. R Singal}, General Topology Relations modern Analysis Algebra, Proc. Kanpur topol. Conf. 1968, 265--296 (1971; Zbl 0234.54008)].
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54F65
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 2171813
zbMATH Keywords: \(R_0\)-space
zbMATH Keywords: \(R_1\)-space
zbMATH Keywords: Wallman compactification
reviewed by: Harald Brandenburg
MaRDI profile type: Publication
OpenAlex ID: W1993308823
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description: scientific article; zbMATH DE number 2171813