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

Year 2016, , 6 - 14, 15.04.2016

Muammer Kula

https://doi.org/10.36753/mathenot.421346

Abstract

There are various generalization of the usual topological T3 and T4- axioms to topological categories

defined in [2] and [8]. [8] is shown that they lead to different T3 and T4 concepts, in general. In this

paper, an explicit characterizations of each of the separation properties T3 and T4 at a point p and the

generalized 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 the

generalized separation properties are examined in this category. Finally, we investigate the relationships

between the generalized separation properties and the separation properties at a point p in this category.

Keywords

Topological category, Cauchy space, Cauchy map, Seperation

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