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A categorical study of compactness via closure
Thesis (MSc (Mathemathical Sciences))--Stellenbosch University, 2009.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Stellenbosch : Stellenbosch University
2009
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| _version_ | 1867614097446535168 |
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| access_status_str | Open Access |
| author | Van Coller, Henry |
| author2 | Holgate, David |
| author_browse | Holgate, David Van Coller, Henry |
| author_facet | Holgate, David Van Coller, Henry |
| author_sort | Van Coller, Henry |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc (Mathemathical Sciences))--Stellenbosch University, 2009. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2351 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:46:37.536Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2009 |
| publishDateRange | 2009 |
| publishDateSort | 2009 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/2351 A categorical study of compactness via closure Van Coller, Henry Holgate, David Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Compactness Closure Kuratowski-Mrowka theorem Theses -- Mathematics Theses -- Applied mathematics Dissertations -- Applied mathematics Dissertations -- Mathematics Topology Mathematical Sciences Mathematics Thesis (MSc (Mathemathical Sciences))--Stellenbosch University, 2009. We have the familiar Kuratowski-Mr owka theorem in topology, where compactness is characterised by a closure and a projection-map (X is compact i p : X Y ! Y is a closed mapping, for any space Y , i.e. p(A) = p(A) A X Y ). Using this as our starting point, we generalise compactness to a categorical setting. We then generalise even further to "asymmetric" compactness. Then we discuss a functional approach to compactness, where we do not explicitly mention closure operators. All this provides economical proofs as well as applications in di erent areas of mathematics. 2009-03-06T12:48:54Z 2010-06-01T08:46:45Z 2009-03-06T12:48:54Z 2010-06-01T08:46:45Z 2009-03 Thesis http://hdl.handle.net/10019.1/2351 en Stellenbosch University application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Compactness Closure Kuratowski-Mrowka theorem Theses -- Mathematics Theses -- Applied mathematics Dissertations -- Applied mathematics Dissertations -- Mathematics Topology Mathematical Sciences Mathematics Van Coller, Henry A categorical study of compactness via closure |
| title | A categorical study of compactness via closure |
| title_full | A categorical study of compactness via closure |
| title_fullStr | A categorical study of compactness via closure |
| title_full_unstemmed | A categorical study of compactness via closure |
| title_short | A categorical study of compactness via closure |
| title_sort | categorical study of compactness via closure |
| topic | Compactness Closure Kuratowski-Mrowka theorem Theses -- Mathematics Theses -- Applied mathematics Dissertations -- Applied mathematics Dissertations -- Mathematics Topology Mathematical Sciences Mathematics |
| url | http://hdl.handle.net/10019.1/2351 |
| work_keys_str_mv | AT vancollerhenry acategoricalstudyofcompactnessviaclosure AT vancollerhenry categoricalstudyofcompactnessviaclosure |