Some generalizations of the Stone Duality Theorem

Abstract

In this paper we obtain some extensions of the Stone Duality Theorem to the categories BoolSp and PerfBoolSp of zero-dimensional locally compact Hausdorff spaces and continuous (respectively, perfect) maps. We also prove some new Stonetype duality theorems for the cofull subcategories of the category BoolSp determined, respectively, by the skeletal maps, quasi-open perfect maps, open maps and open perfect maps.