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Quaestiones Mathematicae

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

Karim Boulabiar

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




http://dx.doi.org/10.2989/16073606.2014.981741
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