Abstract

I’ll talk about a result from the 1930s known as “Stone’s representation theorem for Boolean algebras”. It introduces a link between Boolean algebras and a type of topological spaces called Stone spaces. In the language of category theory (which only appeared later), the result is that the category of Boolean algebras is equivalent to the opposite of the category of Stone spaces.

This has been extended to other classes of topological spaces and partially ordered sets, and these results are now typically referred to as “Stone duality”. In particular Stone duality has been studied in the context of domain theory, and I’ll also mention some of its applications to the semantics of programming languages.

I’ll define all the necessary notions, the only prerequisite is basic category theory.