Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions
This paper studies sequential order convergence and the associated completion in vector lattices of continuous functions. Such a completion for lattices C(X) is realted 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 . This condition is that every dense cozero set S in X should be (^-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 /^-spaces of ).
© 1980 Canadian Mathematical Society
Dashiell, F.; Hager, A.; Henriksen, M. Order-Cauchy completions of rings and vector lattices of continuous functions. Canad. J. Math. 32 (1980), no. 3, 657–685. DOI: 10.4153/CJM-1980-052-0