Completeness properties in the vector lattice C(X)

Abstract

In this thesis we study certain vector lattice properties of the space $C(X)$ of continuous functions on a given topological space X. We show that C(X) is always relatively uniformly complete, and characterize those X for which C(X) is Dedekind complete. We characterise the bands and projection bands in C(X), for X a Tychonoff space, and characterize those Tychonoff spaces X for which C(X) has the projection property.