Order properties of some subalgebras of C(X)
by
Javier Gómez-Pérez
Dpto. Matematicas. Universidad de Leon. Spain

For a completely regular space X, C(X) denotes the algebra of real-valued continuous functions on X and C^*(X) the subalgebra of bounded functions of C(X). A subalgebra A of C(X) containing C^*(X) will be called an intermediate algebra on X. They have been characterized in several ways, one of them by using order properties. Concretely, they are the absolutely convex subalgebras of C(X). They can also be viewed as those algebras obtained by adjoining to C^*(X) a subset F of C(X) so that we get the smallest intermediate algebra containing F. The set F could be finite or countable and in this case those intermediate algebras share a common property; they contain a countable cofinal subset. We establish the difference between these two cases by using a topology similar to one described by Hewitt for C(X) in 1948.

Date received: December 23, 2002