Lattice and algebra homomorphisms on C (X) in Zermelo-Fraenkel set theory

Abstract

Let C (X) denote the lattice-ordered algebra of all real-valued continuous functions on a topological space X. This paper discusses in Zermelo-Fraenkel Set Theory the equivalence on C (X) between algebra homomorphisms, lattice homo- morphisms, and point evaluations.

Keywords: Algebra homomorphism, lattice homomorphism, linear functional, point evaluation, real-valued continuous function, realcompact space, ZF, ZFC