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

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Mathematical Sciences and Applications E-Notes
Volume: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

Pages : 6-14

View : 20 | Download : 13

Publication Date : 2016-04-15

Article Type : Research Paper

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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