A note on almost uniform nearness frames

Abstract

We show that the category of almost uniform nearness frames is co-reflective in the category of all nearness frames with interpolative uniformly below relation. This we do by actually constructing the coreflection. The resulting functor commutes with the uniform coreflection functor. It also commutes with the totally bounded coreflection functor on the subcategory consisting of nearness frames with strong totally bounded coreflection, but not in general, as a counterexample attests.

Quaestiones Mathematicae 34(2011), 247–263.