The Topology of Common Belief ⋆

Abstract. We study the modal logic K4 C 2 of common belief for normal agents. We study Kripke completeness and show that the logic has tree model property. is the modal logic of all TD-intersection As a main result we prove that K4 C 2 closed, bi-topological spaces with derived set interpretation of modalities. Based on the splitting translation we discuss connections with S4 C 2, the logic of common knowledge.