Pre-Hausdorff and Hausdorff Proximity Spaces


Muammer Kula, Samed Özkan, Tugba Maraslı




In this paper, an explicit characterization of the separation properties for 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 for Ti, i = 0, 1, 2 and PreT2 (in our sense), separation properties at a point p and separation properties for Ti, i = 0, 1, 2 in the usual sense in this category.