Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Binary closure operators
Thesis (PhD)--Stellenbosch University, 2016
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
| Published: |
Stellenbosch : Stellenbosch University
2016
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613988856004608 |
|---|---|
| access_status_str | Open Access |
| author | Abdalla, Abdurahman Masoud |
| author2 | Janelidze, Zurab |
| author_browse | Abdalla, Abdurahman Masoud Janelidze, Zurab |
| author_facet | Janelidze, Zurab Abdalla, Abdurahman Masoud |
| author_sort | Abdalla, Abdurahman Masoud |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2016 |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/98843 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:44:53.996Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/98843 Binary closure operators Abdalla, Abdurahman Masoud Janelidze, Zurab Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Mathematics) Binary closure operators Idempotents Categorical closure operators Eilenberg Moore algebra Hereditary hull UCTD Thesis (PhD)--Stellenbosch University, 2016 ENGLISH ABSTRACT : In this thesis we provide a new foundation to categorical closure operators, using more elementary binary closure operators on posets. The original goal of the thesis was to study a categorical closure operator in terms of the family of closure operators on the posets of subobjects. However, this does not allow to express hereditariness, which is an important property of a categorical closure operator. Representing instead a categorical closure operator in terms of the family of binary closure operators on the posets of subobjects, xes this problem. Moreover, the structure of a binary closure operator on a poset is self-dual, unlike that of a unary closure operator or that of a categorical closure operator, and this duality has a useful application in the study of properties of closure operators on categories, where it groups properties of categorical closure operators in dual pairs, and allows to unify results which relate these properties to each other. AFRIKAANSE OPSOMMING : In hierdie tesis verskaf ons, deur gebruik te maak van meer elementêre binêre afsluitingsoperatore op parsiële geordende versamelings, 'n nuwe grondslag tot kategoriese afsluitingsoperatore. Die aanvanklike doel van die tesis was om 'n kategoriese afsluitingsoperator in terme van die familie van afsluitingsoperatore op parsiële die geordende versamelings van subobjekte te bestudeer. Dit laat egter nie toe om oorer ikheid, wat 'n belangrike eienskap van kategoriese operatore is, uit te druk nie. Hierdie probleem word opgelos deur 'n kategoriese operator in terme van die familie van binêre afsluitingsoperatore op parsiële die geordende versamelings van subobjekte te verteenwoordig. Bykomend is die struktuur van 'n binêre afsluitingsoperator op 'n parsiële geordende versameling self-duaal, in teenstelling met di e van 'n unêre of kategoriese afsluitingsoperator. Hierdie dualiteit het 'n nuttige toepassing in die studie van eienskappe van afsluitingsoperatore op kategorieë, waar dit eienskappe van kategoriese afsluitingsoperatore in duale pare groepeer en toelaat dat resultate, wat hierdie eienskappe in verband hou met mekaar, verenig word. Doctoral 2016-03-09T15:08:38Z 2016-03-09T15:08:38Z 2016-03 Thesis http://hdl.handle.net/10019.1/98843 en_ZA Stellenbosch University viii, 97 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Binary closure operators Idempotents Categorical closure operators Eilenberg Moore algebra Hereditary hull UCTD Abdalla, Abdurahman Masoud Binary closure operators |
| title | Binary closure operators |
| title_full | Binary closure operators |
| title_fullStr | Binary closure operators |
| title_full_unstemmed | Binary closure operators |
| title_short | Binary closure operators |
| title_sort | binary closure operators |
| topic | Binary closure operators Idempotents Categorical closure operators Eilenberg Moore algebra Hereditary hull UCTD |
| url | http://hdl.handle.net/10019.1/98843 |
| work_keys_str_mv | AT abdallaabdurahmanmasoud binaryclosureoperators |