In this paper, we give the characterization of closed and strongly closed subsets of an extended pseudo-quasi-semi metric space and show that they induce closure operator. Moreover, we characterize each of Ti , i = 0, 1, 2 and connected extended pseudo-quasi-semi metric spaces and investigate the relationship among them. Finally, we introduce the notion of irreducible objects in a topological category and examine the relationship among each of irreducible, Ti , i = 1, 2, and connected extended pseudo-quasi-semi metric spaces