In the fifties of the previous century, Rasiowa and Sikorski gave a topological proof of Gödel’s completeness theorem for first-order logic. Their proof ultimately relies on the Baire category theorem, which is mainly known for its powerful applications in real and functional analysis. Therefore, the application of Baire’s theorem to prove this fundamental result in logic is a surprising and interesting one. The main goal of this talk will be to give an exposition of this elegant topological proof by Rasiowa and Sikorski.