Van der Walt, Jan Harm2024-07-152024-07-152024-092024-07-12*S2024http://hdl.handle.net/2263/97008Dissertation (MSc (Mathematics))--University of Pretoria, 2024.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.en© 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.UCTDSustainable Development Goals (SDGs)Vector latticeContinuous functionsDedekind completenessProjection bandsBandsSDG-04: Quality EducationNatural and agricultural sciences theses SDG-04Dissertationu18014179