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Completeness properties in the vector lattice C(X)
Dissertation (MSc (Mathematics))--University of Pretoria, 2024.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2024
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| _version_ | 1867613641756377088 |
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| access_status_str | Open Access |
| author2 | Van der Walt, Jan Harm |
| author_browse | Van der Walt, Jan Harm |
| author_facet | Van der Walt, Jan Harm |
| collection | Thesis |
| dc_rights_str_mv | © 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. |
| description | Dissertation (MSc (Mathematics))--University of Pretoria, 2024. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/97008 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:22.809Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/97008 Completeness properties in the vector lattice C(X) Van der Walt, Jan Harm odehyee.kwadwo@gmail.com Schwanke, Chris Afrane-Okese, Kwadwo Nyamedehyee UCTD Sustainable Development Goals (SDGs) Vector lattice Continuous functions Dedekind completeness Projection bands Bands SDG-04: Quality education Natural and agricultural sciences theses SDG-04 Dissertation (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. MasterCard Scholarship Foundation Mathematics and Applied Mathematics MSc (Mathematics) Unrestricted Faculty of Natural and Agricultural Sciences SDG-04: Quality education 2024-07-15T08:52:31Z 2024-07-15T08:52:31Z 2024-09 2024-07-12 Dissertation * S2024 http://hdl.handle.net/2263/97008 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. application/pdf University of Pretoria |
| spellingShingle | UCTD Sustainable Development Goals (SDGs) Vector lattice Continuous functions Dedekind completeness Projection bands Bands SDG-04: Quality education Natural and agricultural sciences theses SDG-04 Completeness properties in the vector lattice C(X) |
| title | Completeness properties in the vector lattice C(X) |
| title_full | Completeness properties in the vector lattice C(X) |
| title_fullStr | Completeness properties in the vector lattice C(X) |
| title_full_unstemmed | Completeness properties in the vector lattice C(X) |
| title_short | Completeness properties in the vector lattice C(X) |
| title_sort | completeness properties in the vector lattice c x |
| topic | UCTD Sustainable Development Goals (SDGs) Vector lattice Continuous functions Dedekind completeness Projection bands Bands SDG-04: Quality education Natural and agricultural sciences theses SDG-04 |
| url | http://hdl.handle.net/2263/97008 |