Local Separation, Closedness and Zero-Dimensionality in Quantale-Valued Reflexive Spaces

Abstract

In this paper, first, we introduce the category Q-RREL consisting of quantale-valued reflexive spaces and Q-monotone mappings, and prove that it is a normalized topological category over SET, the category of sets and functions. Furthermore, we characterize explicitly each of T_i, i=0,1,2 and PreT_2 Q-reflexive spaces and examine the relationships among them. Finally, we give the characterizations of a closed point, (strongly) closed subsets and zero-dimensional objects in this category.