In this paper, the characterization of closed and strongly closed subobjects of an object in category of semiuniform convergence spaces is given and it is shown that they induce a notion of closure which enjoy the basic properties like idempotency,(weak) hereditariness, and productivity in the category of semiuniform convergence spaces. Furthermore, T1 semiuniform convergence spaces with respect to these two new closure operators are characterized.

In this paper, we characterize local pre-Hausdor¤ extended pseudoquasi-semi metric spaces and investigate the relationships between them. Finally, we show that local pre-Hausdor¤ extended pseudo-quasi-semi metric spaces are hereditary and productive.

In this paper, we characterize various local T 2 extended pseudoquasi-semi metric spaces and investigate the relationships among these various forms. Finally, we give some invariance properties of these local T 2 extended pseudo-quasi-semi metric spaces.

Highlights • We characterized each of local ̅ 3 (resp. 3 ′, ̅ 3 , 3 ′) constant filter convergence spaces. • We investigated the relationships among these various forms. • We showed that the categories ̅ 3 and ̅ 3 were isomorphic categories. • We showed that the categories 3 ′ and 3 ′ were isomorphic categories.

In this paper, we characterize various local forms of T4 constant filter convergence spaces and investigate the relationships among them as well as show that the full subcategories of the category of constant filter convergence spaces consisting of local T4 constant filter convergence spaces are hereditary. Furthermore, we examine the relationship between local T4 and general T4 constant filter convergence spaces. Finally, we present Urysohn's Lemma and Tietze Extension Theorem for constant filter convergence spaces.