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This paper is a summary of joint research by F. Dashiell, A. Hager and the present author. Proofs are largely omitted. A complete version will appear in the Canadian Journal of Mathematics. It is devoted to a study of sequential order-Cauchy convergence and the associated completion in vector lattices of continuous functions. Such a completion for lattices C(X) is related to certain topological properties of the space X and to ring properties of C(X). The appropriate topological condition on the space X equivalent to this type of completeness for the lattice C(X) was first identified for compact spaces X in [D]. This condition is that every dense cozero set S in X should be C*-embedded in X (that is, all bounded continuous functions on S extend to X). We call Tychonoff spaces X with this property quasi-F spaces (since they generalize the F-spaces of [GH]).


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© 1979 Topology Proceedings, Auburn University Department of Mathematics

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