Published online by Cambridge University Press: 20 November 2018
Throughout, topological spaces are assumed to be completely regular. C(X) (resp. C*(X)) will denote the ring of all (resp. all bounded) continuous real-valued functions. βX will denote the Stone-Cech compactification of X. In [2], Nel and Riorden defined C≠(X) to be the set of all f ∊ C(X) such that M(f) is real in the residue class ring C(X)/M for every maximal ideal M in C(X). C≠(X) is a subalgebra as well as a sublattice of C*(X).
This paper is a part of the author's Ph.D. thesis at the University of British Columbia written under the supervision of J. V. Whittaker.