an:05051839
Zbl 1098.54018
Tallafha, Abdalla; Al-Bsoul, Adnan; Fora, Ali
Closurely ordered countable sets and applications
EN
Glob. J. Pure Appl. Math. 1, No. 2, 177-182 (2005).
00126807
2005
j
54D10 54D99 54F65 54G20
lower separation axioms; CDH space; COP; COCS
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 \textit{B. Fitzpatrick jun.}, \textit{J. M. S. White} and \textit{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.
Zbl 0767.54018; Zbl 0767.54013