## The modal logic of continuous functions on the rational numbers

Let ℒ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality ⬛ and a temporal modality ○, understood as 'next'. We extend the topological semantic for S4 to a semantics for the
language ℒ by interpreting ℒ in *dynamic topological systems*, i.e., ordered pairs ⟨ *X, f* ⟩, where *X* is a topological space and *f* is a continuous function on *X*. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown that S4C is sound and complete for this semantics. Zhang and Mints have shown that S4C is complete relative to a particular topological
space, Cantor space. The current paper produces an alternate proof of
the Zhang-Mints result.