Article

On characterizing the pointfree function ring reflection in terms of uniformities

Published in: Quaestiones Mathematicae
Volume 40, issue 7, 2017 , pages: 985–990
DOI: 10.2989/16073606.2017.1339740
Author(s): B. BanaschewskiDepartment of Mathematics and Statistics, Canada

Abstract

Given that the -rings ℜL of real-valued continuous functions on completely regular frames L are monoreflective in the category of all archimedean f-rings with unit, one can ask how a sub--ring A with unit of some ℜL has to be related to L to make ℜL the corresponding reflection of A. This note provides an answer in terms of a uniformity on L naturally determined by A, and then establishes the analogous result for the -ring ℨL of real-valued continuous functions on 0-dimensional frames and the archimedean f-rings with singular unit.

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