On coreflective hulls in [0; 1]-TOP and <i>s</i>[0; 1]-TOP

Abstract

In this paper, we find the coreflective hull of the category of indiscrete [0; 1]-topological spaces in the category [0; 1]-TOP of [0; 1]-topological spaces. We also show that the coreflective hull of a single-point s[0; 1]-topological space in the category s[0; 1]-TOP of stratified [0; 1]-topological spaces is the category of discrete [0; 1]-topological spaces and the coreflective hull of the category of indiscrete s[0; 1]-topological spaces in s[0; 1]-TOP is the category s[0; 1]-IG-TOP of indiscrete-generated stratified [0; 1]-topological spaces.

Keywords: Coreflective subcategory, coreflective hull, complete atomic Boolean algebra

Quaestiones Mathematicae 36(2013), 167–179