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Semi-order units in vector lattices
Dissertation (MSc (Mathematics))--University of Pretoria, 2021.
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| Other Authors: | |
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613530333642752 |
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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 | © 2022 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, 2021. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/84700 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:36.798Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| 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:2263/84700 Semi-order units in vector lattices Van der Walt, Jan Harm u16124970@tuks.co.za Wortel, Marten Chitanga, Painos UCTD Vector Lattices Semi-order units Continuous functions Dissertation (MSc (Mathematics))--University of Pretoria, 2021. The space C(X) of real-valued continuous functions on a topological space X is a vector lattice and a locally convex topological vector space, but what is the interaction between these structures? In the case of a compact space X, the norm and the order are closely related to one another. Indeed, one may define the norm through the order structure. We aim to generalize these results to a non-compact space. Let X be a Tychonoff space and consider C(X) equipped with the compact-open topology. We will establish a relationship between this topology and the order structure on C(X) Mastercard Foundation Scholarship Mathematics and Applied Mathematics MSc (Mathematics) Unrestricted 2022-03-30T09:37:26Z 2022-03-30T09:37:26Z 2022-09 2021 Dissertation * S2022 http://hdl.handle.net/2263/84700 en © 2022 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 Vector Lattices Semi-order units Continuous functions Semi-order units in vector lattices |
| title | Semi-order units in vector lattices |
| title_full | Semi-order units in vector lattices |
| title_fullStr | Semi-order units in vector lattices |
| title_full_unstemmed | Semi-order units in vector lattices |
| title_short | Semi-order units in vector lattices |
| title_sort | semi order units in vector lattices |
| topic | UCTD Vector Lattices Semi-order units Continuous functions |
| url | http://hdl.handle.net/2263/84700 |