Tallafha, Abdalla; Al-Bsoul, Adnan; Fora, Ali Closurely ordered countable sets and applications. (English) Zbl 1098.54018 Glob. J. Pure Appl. Math. 1, No. 2, 177-182 (2005). 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. Cited in 1 Document MSC: 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 Keywords:lower separation axioms; CDH space; COP; COCS PDF BibTeX XML Cite \textit{A. Tallafha} et al., Glob. J. Pure Appl. Math. 1, No. 2, 177--182 (2005; Zbl 1098.54018) Full Text: Link