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 local Ti, i = 0, 1, 2 and PreT2 Q-reflexive spaces and examine the relationships among them. Finally, we give the characterizations of (strongly) closed subsets and zero-dimensional objects in this category.