A unified view of the Dedekind completion of pointfree function rings

  • Javier Gutiérrez García
  • Imanol Mozo Carollo
  • Jorge Picado
Keywords: Frame, locale, frame of reals, continuous real function, function ring, order complete, Dedekind completion, scale, normal semicontinuous real function, partial real function, Hausdorff continuous real function, cb-fram

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.

Mathematics Subject Classification (2010): Primary: 06D22; Secondary: 26A15, 54C30, 54D15.

Keywords: Frame, locale, frame of reals, continuous real function, function ring, order complete, Dedekind completion, scale, normal semicontinuous real function, partial real function, Hausdorff continuous real function, cb-frame.

Published
2016-11-25
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606