Local $T_3$ Constant Filter Convergence Spaces

Abstract

In this paper, we characterize each of local $T_3$(resp. 𝑇3′, 𝑆𝑇̅3, 𝑆𝑇3′) constant filter convergencespaces and investigate the relationships among these various forms. We show that the fullsubcategories 𝑇̅3𝐶𝑜𝑛𝐹𝐶𝑂 and 𝑆𝑇̅3𝐶𝑜𝑛𝐹𝐶𝑂 (resp. 𝑇3′𝐶𝑜𝑛𝐹𝐶𝑂 and 𝑆𝑇3′𝐶𝑜𝑛𝐹𝐶𝑂) of 𝐶𝑜𝑛𝐹𝐶𝑂 areisomorphic categories. Moreover, we show that if a constant filter convergence space (B,K) is 𝑇̅3(resp. 𝑇3′, 𝑆𝑇̅3 or 𝑆𝑇3′) at p and M⊂B with p∈M, then M is 𝑇̅3 (resp. 𝑇3′) at p