Abstract:Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.
Keywords: Booleanization, uniform frame, uniform space, weakly open maps and homomorphisms
AMS Subject Classification: 06D10, 06E15, 18A40, 18B30, 54C10, 54E15