Completeness properties in the vector lattice C(X)
| dc.contributor.advisor | Van der Walt, Jan Harm | |
| dc.contributor.coadvisor | Schwanke, Chris | |
| dc.contributor.email | odehyee.kwadwo@gmail.com | en_US |
| dc.contributor.postgraduate | Afrane-Okese, Kwadwo Nyamedehyee | |
| dc.date.accessioned | 2024-07-15T08:52:31Z | |
| dc.date.available | 2024-07-15T08:52:31Z | |
| dc.date.created | 2024-09 | |
| dc.date.issued | 2024-07-12 | |
| dc.description | Dissertation (MSc (Mathematics))--University of Pretoria, 2024. | en_US |
| dc.description.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. | en_US |
| dc.description.availability | Unrestricted | en_US |
| dc.description.degree | MSc (Mathematics) | en_US |
| dc.description.department | Mathematics and Applied Mathematics | en_US |
| dc.description.faculty | Faculty of Natural and Agricultural Sciences | en_US |
| dc.description.sdg | SDG-04: Quality Education | en_US |
| dc.description.sponsorship | MasterCard Scholarship Foundation | en_US |
| dc.identifier.citation | * | en_US |
| dc.identifier.other | S2024 | en_US |
| dc.identifier.uri | http://hdl.handle.net/2263/97008 | |
| dc.language.iso | en | en_US |
| dc.publisher | University of Pretoria | |
| dc.rights | © 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. | |
| dc.subject | UCTD | en_US |
| dc.subject | Sustainable Development Goals (SDGs) | en_US |
| dc.subject | Vector lattice | en_US |
| dc.subject | Continuous functions | en_US |
| dc.subject | Dedekind completeness | |
| dc.subject | Projection bands | |
| dc.subject | Bands | |
| dc.subject.other | SDG-04: Quality Education | |
| dc.subject.other | Natural and agricultural sciences theses SDG-04 | |
| dc.title | Completeness properties in the vector lattice C(X) | en_US |
| dc.type | Dissertation | en_US |