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We investigate the topological interpretation of modal logic in modern terms, using a new notion of bisimulation. We look at modal logics with interesting topological content, presenting, among others, a new proof of McKinsey and Tarski's theorem on completeness of  S4  with respect to the real line, and a completeness proof for the logic of finite unions of convex sets of reals. We conclude with a broader picture of extended modal languages of space, for which the main logical questions are still wide open.

Reasoning About Space: The Modal Way