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Syntopogenous structures and real-compactness
The syntopogenous structures were introduced by Á. Császár. These are generalisations of classical continuity structures such as topologies, proximities and uniformities. In his book, Foundations of General Topology (1963) (Preceded by a French (1960) and a German (1963) edition), Császár treated ma...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613261647577088 |
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| access_status_str | Open Access |
| author | Flax, Cyril Lee |
| author2 | Brümmer, Guillaume C L |
| author_browse | Brümmer, Guillaume C L Flax, Cyril Lee |
| author_facet | Brümmer, Guillaume C L Flax, Cyril Lee |
| author_sort | Flax, Cyril Lee |
| collection | Thesis |
| description | The syntopogenous structures were introduced by Á. Császár. These are generalisations of classical continuity structures such as topologies, proximities and uniformities. In his book, Foundations of General Topology (1963) (Preceded by a French (1960) and a German (1963) edition), Császár treated many properties of syntopgenous structures. Among these properties were completeness and compactness, but not realcompactness. Our purpose was to extend the definition of realcompactness from uniformisable topologies to arbitrary syntopogenous structures and to produce a real compact reflection for arbitrary syntopogenous structures. We did not fully accomplish this purpose. We have, in fact, first defined a notion of quasirealcompactness for arbitrary syntopogenous structures. For uniformisable Hausdorff topologies, realcompactness implies quasirealcompactness; we could not prove or disprove the converse implication. Nevertheless, we were able to give a characterisation of realcompactness for a uniformisable Hausdorff topology in terms of quasirealcompactness of a certain induced proximity; moreover, we produced a double quasirealcompact reflection in the category of separated syntopogenous structures, and from this retrieved the classical Hewitt realcompact reflection. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/18367 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:19.547Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/18367 Syntopogenous structures and real-compactness Flax, Cyril Lee Brümmer, Guillaume C L Mathematics Topology The syntopogenous structures were introduced by Á. Császár. These are generalisations of classical continuity structures such as topologies, proximities and uniformities. In his book, Foundations of General Topology (1963) (Preceded by a French (1960) and a German (1963) edition), Császár treated many properties of syntopgenous structures. Among these properties were completeness and compactness, but not realcompactness. Our purpose was to extend the definition of realcompactness from uniformisable topologies to arbitrary syntopogenous structures and to produce a real compact reflection for arbitrary syntopogenous structures. We did not fully accomplish this purpose. We have, in fact, first defined a notion of quasirealcompactness for arbitrary syntopogenous structures. For uniformisable Hausdorff topologies, realcompactness implies quasirealcompactness; we could not prove or disprove the converse implication. Nevertheless, we were able to give a characterisation of realcompactness for a uniformisable Hausdorff topology in terms of quasirealcompactness of a certain induced proximity; moreover, we produced a double quasirealcompact reflection in the category of separated syntopogenous structures, and from this retrieved the classical Hewitt realcompact reflection. 2016-03-30T07:08:28Z 2016-03-30T07:08:28Z 1972 Master Thesis Masters MSc http://hdl.handle.net/11427/18367 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Topology Flax, Cyril Lee Syntopogenous structures and real-compactness |
| thesis_degree_str | Master's |
| title | Syntopogenous structures and real-compactness |
| title_full | Syntopogenous structures and real-compactness |
| title_fullStr | Syntopogenous structures and real-compactness |
| title_full_unstemmed | Syntopogenous structures and real-compactness |
| title_short | Syntopogenous structures and real-compactness |
| title_sort | syntopogenous structures and real compactness |
| topic | Mathematics Topology |
| url | http://hdl.handle.net/11427/18367 |
| work_keys_str_mv | AT flaxcyrillee syntopogenousstructuresandrealcompactness |