- Mathematical Sciences and Applications E-Notes
- Vol: 4 Issue: 1
- T3 and T4-Objects at p in the Category of Cauchy Spaces
T3 and T4-Objects at p in the Category of Cauchy Spaces
Authors : Muammer Kula
Pages : 6-14
Doi:10.36753/mathenot.421346
View : 7 | Download : 6
Publication Date : 2016-04-15
Article Type : Research
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