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Structured frames
Bibliography: pages 141-144.
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613140636663808 |
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| access_status_str | Open Access |
| author | Frith, John L |
| author2 | Hardie, K A |
| author_browse | Frith, John L Hardie, K A |
| author_facet | Hardie, K A Frith, John L |
| author_sort | Frith, John L |
| collection | Thesis |
| description | Bibliography: pages 141-144. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17589 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:24.573Z |
| 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:11427/17589 Structured frames Frith, John L Hardie, K A Mathematics Topology Bibliography: pages 141-144. Ehresmann in 1959 first articulated the view that a complete lattice with an appropriate distributivity property deserved to be studied as a generalized topological space in its own right. He called the lattice a local lattice. Here is the distributivity property: x ∧ Vxα = V(x∧xα). A map of local lattices should preserve finite meets and arbitrary joins (and hence top and bottom elements). Dowker and Papert introduced the term frame for a local lattice and extended many results of topology to frame theory. At the 1981 international conference on categorical algebra and topology at Cape Town University a suggestion was made that a study of "uniform frames" (whatever they might be) would be an appropriate and useful start to a project concerned with examining, from a lattice theoretical point of view, the many topological structures which have gained acceptance in the topologist's arsenal of useful tools. It was felt that many of the pre-requisites for such a study had been established, and in fact one of the themes of the conference was the growing role of lattice theory in topology. The suggestion was eagerly accepted, and this thesis is the result. 2016-03-09T09:01:05Z 2016-03-09T09:01:05Z 1986 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/17589 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Topology Frith, John L Structured frames |
| thesis_degree_str | Doctoral |
| title | Structured frames |
| title_full | Structured frames |
| title_fullStr | Structured frames |
| title_full_unstemmed | Structured frames |
| title_short | Structured frames |
| title_sort | structured frames |
| topic | Mathematics Topology |
| url | http://hdl.handle.net/11427/17589 |
| work_keys_str_mv | AT frithjohnl structuredframes |