Stone Representation Theorem

The theorem stating that every Boolean algebra is isomorphic to an algebra of sets: concretely, it is isomorphic to the algebra of clopen (simultaneously closed and open) subsets of a compact, totally disconnected Hausdorff topological space (the Stone space of the algebra).

A theorem establishing a dual equivalence between the category of Boolean algebras and the category of zero-dimensional compact Hausdorff spaces (Stone spaces) by representing each Boolean algebra as the algebra of clopen subsets of a canonical compact space of ultrafilters.