The order topology for function lattices and realcompactness

[摘要] A latticeK(X,Y)of continuous functions on spaceXis associated to each compactificationYofX. It is shown forK(X,Y)that the order topology is the topology of compact convergence onXif and only ifXis realcompact inY. 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 everyC(X)and all countably universally complete function lattices with 1. It is shown that a choice ofK(X,Y)endowed with a natural convergence structure serves as the convergence space completion ofVwith the relative uniform convergence.

[学科分类] 数学（综合）