Pre-Hausdorff and Hausdorff Proximity Spaces

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