In this paper, we characterize both closed and strongly closed subobjects in the category of bounded uniform filter spaces and introduce two notions of closure operators which satisfy weakly hereditary, idempotent and productive properties. We further characterize each of Tj (j= 0,1) bounded uniform filter spaces using these closure operators and examine that each of them form quotient-reflective subcategories of the category of bounded uniform filter spaces. Also, we characterize connected bounded uniform filter spaces. Finally, we introduce ultraconnected objects in topological category and examine the relationship among irreducible, ultraconnected and connected bounded uniform filter spaces.

<abstract><p>Previously, several notions of $ T_{0} $ and $ T_{1} $ objects have been studied and examined in various topological categories. In this paper, we characterize each of $ T_{0} $ and $ T_{1} $ objects in the categories of several types of bounded uniform filter spaces and examine their mutual relations, and compare that with the usual ones. Moreover, it is shown that under $ T_{0} $ (resp. $ T_{1} $) condition, the category of preuniform (resp. semiuniform) convergence spaces and the category of bornological (resp. symmetric) bounded uniform filter spaces are isomorphic. Finally, it is proved that the category of each of $ T_{0} $ (resp. $ T_{1} $) bounded uniform filter space are quotient reflective subcategories of the category of bounded uniform filter spaces.</p></abstract>