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Closurely ordered countable sets and applications. (English) Zbl 1098.54018
Summary: We order a countable set by means of closure. As an application of this technique we obtain some characterizations of \(T_0\) and \(T_1\)-spaces. Also, we give another proof of the result of B. Fitzpatrick jun., J. M. S. White and H. Zhou in [Topology Appl. 44, 143–147 (1992; Zbl 0767.54013)] which states that every CDH space is \(T_1\), throughout closurely ordered countable sets. Moreover, the technique used in the proof is programmable and expected to have applications in computer sciences.

54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D99 Fairly general properties of topological spaces
54F65 Topological characterizations of particular spaces
54G20 Counterexamples in general topology
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