Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions

Authors

F. Dashiell
A. Hager
Melvin Henriksen, Harvey Mudd CollegeFollow

Document Type

Article

Department

Mathematics (HMC)

Publication Date

1980

Abstract

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 [6]. 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 [12]).

Rights Information

© 1980 Canadian Mathematical Society

DOI

10.4153/CJM-1980-052-0

Recommended Citation

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