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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.

##### 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
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