On epireflective and coreflective hulls of a particular L-topological space

Abstract

Abstract. In this paper, we study some aspects of the category L-ZTop of zero- dimensional L-topological spaces. After noting that it is a topological category, we identify a `Sierpinski object' L_Z in it. We further show that two epireflective hulls of L_Z respectively turn out to be the categories of zero-dimensional T₀-L-topological spaces and of zero-dimensional sober L-topological spaces. We also determine the coreflective hull of L_Z in the category of L-topological spaces.

Mathematics Subject Classication (2010): 03E72, 18A40, 54A40.

Keywords: L-topology, T₀-L-topological space, zero-dimensional L-topological space, epireflective hull, coreflective hull