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T_2-Objects In Categories Of Filter And Local Filter Convergence Spaces, M. Baran

Turkish Journal of Mathematics

There are various generalizations of the usual T_2 (Hausdorff) axiom of topology to an arbitrary topological category defined in [1]. In this paper, four more new generalizations of Hausdorff spaces are given in the topological categories. Moreover, the relationships among all of these T_2 structures and the ones given in [5] and [7] as well as some invariance properties of them are investigated in the categories of filter and local filter convergence spaces. Keywords: Topological Categories, T_2-objects, Filter Convergence Spaces.