Two extensions of the Stone Duality to the category of zero-dimensional Hausdorff spaces

Abstract

Extending the Stone Duality Theorem, we prove two duality theorems for
the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. Both of them imply easily the Tarski Duality Theorem,
as well as two new duality theorems for the category EDTych of extremally disconnected Tychonoff spaces and continuous maps.
Also, we describe  two categories which are dually equivalent to the category
ZComp of zero-dimensional Hausdorff compactifications of
zero-dimensional Hausdorff spaces and obtain as a corollary the Dwinger Theorem about zero-dimensional compactifications of a zero-dimensional
Hausdorff space.