Stone functor

From Wikipedia, the free encyclopedia

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

[edit] See also

• Stone's representation theorem for Boolean algebras

[edit] References

• Abstract and Concrete Categories. The Joy of Cats. Jiri Adámek, Horst Herrlich, George E. Strecker.