International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1981 / Article

Open Access

Volume 4 |Article ID 268918 | https://doi.org/10.1155/S0161171281000173

W. A. Feldman, J. F. Porter, "The order topology for function lattices and realcompactness", International Journal of Mathematics and Mathematical Sciences, vol. 4, Article ID 268918, 16 pages, 1981. https://doi.org/10.1155/S0161171281000173

The order topology for function lattices and realcompactness

Received12 Jun 1980

Abstract

A lattice K(X,Y) of continuous functions on space X is associated to each compactification Y of X. It is shown for K(X,Y) that the order topology is the topology of compact convergence on X if and only if X is realcompact in Y. 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 C(X) and all countably universally complete function lattices with 1. It is shown that a choice of K(X,Y) endowed with a natural convergence structure serves as the convergence space completion of V with the relative uniform convergence.

Copyright © 1981 Hindawi Publishing Corporation. 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.


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