In topology, and related areas of mathematics, a Stone space is a non-empty compact totally disconnected Hausdorff space. Such spaces are also called profinite spaces. They are named after Marshall Harvey Stone.
A form of Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to the Boolean algebra of clopen sets of a Stone space. This isomorphism forms a category-theoretic duality between the categories of Boolean algebras and Stone spaces.
Equivalently, Stone space is a topological space such that:
- Compact, totally separated;
- Compact, , zero-dimensional;
- Coherent and Hausdorff.