  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.
