Completeness properties in the vector lattice C(X)

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Completeness properties in the vector lattice C(X)

Afrane-Okese, Kwadwo Nyamedehyee
URI: http://hdl.handle.net/2263/97008
Date: 2024-07-12

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.

Description:

Dissertation (MSc (Mathematics))--University of Pretoria, 2024.

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