**Modality as Topology: Completeness for S4**

In 1944, Alfred Tarski and J. C. C. McKinsey pointed out that possibility can be modeled topologically. The idea is to think of possibility as a kind of continuity: Q is possible at the P worlds just in case there are Q worlds that are continuous with the P worlds. These notes walk through the McKinsey and Tarski’s proof that S4 is complete when using topological semantics.