  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.
