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
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.
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