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There are various generalization of the usual topological T3 and T4 axioms to topological categories defined in [2] and [7]. [7] is shown that they lead to different T3 and T4 concepts, in general. In this paper, an explicit characterization of each of the separation properties T3 and T4 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 are examined in this category.

T3 AND T4-objects in the topological category of cauchy spaces