Stone functor

In mathematics, the Stone functor is a functor "S": Topop → Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras and Boolean homomorphisms. It assigns to each topological space "X" the Boolean algebra "S"("X") of its clopen subsets, and to each morphism "f"op: "X" → "Y" in Topop (i.e., a continuous map "f": "Y" → "X") the homomorphism "S"("f"): "S"("X") → "S"("Y") given by "S"("f")("Z") = "f"−1["Z"].