Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Local connectedness of frames
In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2023
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613170618597376 |
|---|---|
| access_status_str | Open Access |
| author | Mushaandja, Zechariah |
| author2 | Schauerte, Anneliese |
| author_browse | Mushaandja, Zechariah Schauerte, Anneliese |
| author_facet | Schauerte, Anneliese Mushaandja, Zechariah |
| author_sort | Mushaandja, Zechariah |
| collection | Thesis |
| description | In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/38321 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:53.390Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| 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:11427/38321 Local connectedness of frames Mushaandja, Zechariah Schauerte, Anneliese mathematics and applied mathematics In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5. 2023-08-29T11:40:15Z 2023-08-29T11:40:15Z 2004 2023-08-29T11:39:57Z Master Thesis Masters MSc http://hdl.handle.net/11427/38321 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | mathematics and applied mathematics Mushaandja, Zechariah Local connectedness of frames |
| thesis_degree_str | Master's |
| title | Local connectedness of frames |
| title_full | Local connectedness of frames |
| title_fullStr | Local connectedness of frames |
| title_full_unstemmed | Local connectedness of frames |
| title_short | Local connectedness of frames |
| title_sort | local connectedness of frames |
| topic | mathematics and applied mathematics |
| url | http://hdl.handle.net/11427/38321 |
| work_keys_str_mv | AT mushaandjazechariah localconnectednessofframes |