\(T_{(\alpha,\beta)}\)-spaces and the Wallman compactification
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)].
scientific article; zbMATH DE number 2171813
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