Articles

A note on almost uniform nearness frames

Published in: Quaestiones Mathematicae
Volume 34, issue 2, 2011 , pages: 247–263
DOI: 10.2989/16073606.2011.594239
Author(s): Themba DubeDepartment of Mathematical Sciences, South Africa, MartinM. MugochiDepartment of Mathematics, Namibia

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.

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