T3 and T4-Objects at p in the Category of Cauchy Spaces

Abstract

There are various generalization of the usual topological T3 and T4- axioms to topological categoriesdefined in [2] and [8]. [8] is shown that they lead to different T3 and T4 concepts, in general. In thispaper, an explicit characterizations of each of the separation properties T3 and T4 at a point p and thegeneralized separation properties is given in the topological category of Cauchy spaces. Moreover,specific relationships that arise among the various Ti, i = 0; 1; 2; 3; 4, PreT2; and T2 structures at p and thegeneralized separation properties are examined in this category. Finally, we investigate the relationshipsbetween the generalized separation properties and the separation properties at a point p in this category.