Stone functor

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Stone functor.svg

In mathematics, the Stone functor is a functor S: TopopBool, 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 fop: XY in Topop (i.e., a continuous map f: YX) the homomorphism S(f): S(X) → S(Y) given by S(f)(Z) = f−1[Z].

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