Syntopogenous spaces with preorder. III: Separation (Q1060726)

In this third paper [see also the preceding review] devoted to the study of syntopogenous spaces with preorder the author introduces two separation axioms; one of which is weaker, the other is stronger than the separation axiom of \textit{D. C. J. Burgess} and \textit{M. Fitzpatrick} [Math. Proc. Camb. Phil. Soc. 83, 19-24 (1978; Zbl 0389.54002)]. The most important properties of these \(T_ i\)-preordered syntopogenous spaces (for \(i=0,1,2)\) are examined, including a generalization of the quotient space corresponding to the separative partition of a syntopogenous space. It is shown that the category of the \(T_ 0\)-ordered syntopogenous spaces is epireflective in the category of all preordered syntopogenous spaces and continuous preorder preserving mappings.