International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 2, Pages 289-304
The order topology for function lattices and realcompactness
Department of Mathematics, University of Arkansas, Fayetteville 72701, AR, USA
Received 12 June 1980
Copyright © 1981 W. A. Feldman and J. F. Porter. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A lattice of continuous functions on space is associated to each compactification of . It is shown for that the order topology is the topology of compact convergence on if and only if is realcompact in . This result is used to provide a representation of a class of vector lattices with the order topology as lattices of continuous functions with the topology of compact convergence. This class includes every and all countably universally complete function lattices with 1. It is shown that a choice of endowed with a natural convergence structure serves as the convergence space completion of with the relative uniform convergence.