The Propositional Theory of Closure

Abstract

We study the simplest fragment of topological theory: those statements that can be expressed using one set variable, interior and closure operators, and inclusion. We introduce a formal system that is simple enough to be implemented on a computer and exhaustively studied and yet rich enough to be sound and complete for the fragment of theory under consideration. This fragment is rich enough to capture concepts such as regular open sets, extremal disconnectedness, partition topologies, and the nodec property.