Separation properties at p for the topological category of Cauchy spaces

Abstract

An explicit characterization of each of the separation properties Ti, i=0,1, \(\mathop {\mathrm {Pre}}\nolimits T_{2}\), and T2 at a point p is given in the topological category of Cauchy spaces. Moreover, specific relationships that arise among the various Ti, i=0,1, \(\mathop {\mathrm {Pre}}\nolimits T_{2}\), and T2 structures at p are examined in this category. Finally, we investigate the relationships between generalized separation properties and separation properties at a point p in this category.