ABSTRACT
In this chapter, the authors present a theorem that generalizes the theorem to Riesz spaces (together with modes of convergence) which can be appropriately represented as continuous extended real-valued functions. Such representable spaces include Banach lattices with quasi-interior points, so that theorem encompasses a result due to Schaefer. Theorem applies more generally to Banach lattices having topological orthogonal systems or having topological order partitions. By a function algebra the authors mean an Archimedean F-algebra having no nonzero nilpotent elements. Although one can define the bounded elements in a function algebra abstractly, they can be recognized as the bounded functions. The authors show that the Johnson representation is an appropriate representation for their purposes.
