Quotient reflective subcategories of the category of bounded uniform filter spaces.

Previously, several notions of T₀ and T₁ objects have been studied and examined in various topological categories. In this paper, we characterize each of T₀ and T₁ 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 T₀ (resp. T₁) 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 T₀ (resp. T₁) bounded uniform filter space are quotient reflective subcategories of the category of bounded uniform filter spaces. [ABSTRACT FROM AUTHOR]