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 previous papers, various notions of T 0 and T 1 objects in a topological category were introduced and compared. In this paper, we characterize each of these classes of objects in categories of various types of uniform convergence spaces and compare them with the usual ones as well as examine how these generalizations are related.

There are various forms of Tychonoff objects for an arbitrary set-based topological category. In this paper, any explicit characterization of each of the Tychonoff Objects is given in the topological category of Cauchy spaces. Moreover, we characterize each of them for the category of Cauchy spaces and investigate the relationships among the various T i , i = 0, 1, 2, 3, 4, P reT 2 , and T 2 (we will refer to it as the usual one) structures are examined in this category.