Generalized Vietoris Bisimulations

Abstract: We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4]. The main result of our paper is that bisimulation for a $\mathbf{Stone}$ coalgebra is the topological closure of bisimulation for the underlying $\mathbf{Set}$ coalgebra.