Pre-Hausdorff and Hausdorff Proximity Spaces

Abstract

In this paper, an explicit characterization of the separation properties T0, T1, PreT2 (pre-Hausdorff) and T2 (Hausdorff) is given in the topological category of proximity spaces. Moreover, specific relationships that arise among the various Ti, i = 0; 1; 2 and PreT2 structures are examined in this category.
Finally, we investigate the relationships among generalized separation properties Ti, i = 0; 1; 2 and PreT2 (in our sense), separation properties at a point p and separation properties Ti, i = 0; 1; 2 in the usual sense in this category.