Local T_3 Constant Filter Convergence Spaces

Abstract

In this paper, we characterize each of local T_3(resp. T_3', ST _3, ST_3') constant filter convergence spaces and investigate the relationships among these various forms. We show that the full subcategories T_3 ConFCO and ST_3 ConFCO (resp. T_3'ConFCO and ST_3'ConFCO) of ConFCO are isomorphic categories. Moreover, we show that if a constant filter convergence space (B,K) is T _3 (resp. T_3^' , ST _3 or ST_3') at p and M⊂B with p∈M, then M is T _3 (resp. T_3^' ) at p.

Keywords

• Topological category,Convergence spaces,PreHausdorff spaces,T_3 spaces

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