Extending the Stone Duality Theorem, we prove two duality theorems for the
category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. They
extend also the Tarski Duality Theorem; the latter is even derived from one
of them. We prove as well 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.