Article

A unified view of the Dedekind completion of pointfree function rings

Published in: Quaestiones Mathematicae
Volume 39 , issue 7 , 2016 , pages: 991–1003

DOI: 10.2989/16073606.2016.1241959

Author(s): Javier Gutiérrez García Department of Mathematics, Spain , Imanol Mozo Carollo Department of Mathematics, Spain , Jorge Picado CMUC, Department of Mathematics, Portugal

Keywords: Primary: 06D22 , Secondary: 26A15 , 54C30 , 54D15 , Primary: 06D22 , Secondary: 26A15 , 54C30 , 54D15

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Abstract

We provide the appropriate unifying framework for the various descriptions of the Dedekind completion of the ring C(L) of continuous real functions on a frame L. It is based on suitable Galois connections and a general result about Galois connections, showing once more the ubiquity of (Galois) adjunctions between partially ordered sets and their conceptual simplicity and eﬀectiveness.

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