Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Transitive quasi-uniform spaces
Chapter 1 deals with basic properties of the category of quasi-uniform spaces and its full subcategory Qut of transitive quasi-uniform spaces. Chapter 2 concerns Fletcher's construction. We extend the class of covers to which this construction may be applied and study the functoriality of the constr...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2016
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613324694257664 |
|---|---|
| access_status_str | Open Access |
| author | Halpin, Michael Norman |
| author2 | Brümmer, Guillaume C L |
| author_browse | Brümmer, Guillaume C L Halpin, Michael Norman |
| author_facet | Brümmer, Guillaume C L Halpin, Michael Norman |
| author_sort | Halpin, Michael Norman |
| collection | Thesis |
| description | Chapter 1 deals with basic properties of the category of quasi-uniform spaces and its full subcategory Qut of transitive quasi-uniform spaces. Chapter 2 concerns Fletcher's construction. We extend the class of covers to which this construction may be applied and study the functoriality of the construction. The major result is that every right inverse of the forgetful functor Qut--->Top is obtainable by the extended Fletcher construction. In Chapter 3 we characterize pairwise zero dimensional bitopological spaces as those admitting transitive quasi-uniformities. An initiality characterization of pairwise zero dimensional bitopological spaces suggested by Brümmer leads to a description of the coarsest right inverse of the forgetful functor. In Chapter 4 we discuss countably based transitive quasi-uniformities, in that they relate to quasi-metrization. We elaborate on a result of Fletcher and Lindgren (1972) and obtain a bitopological analogue. In Chapter 5 we bring together a number of topics which relate to our previous chapters and point to further questions. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/18241 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:20.437Z |
| 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:11427/18241 Transitive quasi-uniform spaces Halpin, Michael Norman Brümmer, Guillaume C L Mathematics Topology Chapter 1 deals with basic properties of the category of quasi-uniform spaces and its full subcategory Qut of transitive quasi-uniform spaces. Chapter 2 concerns Fletcher's construction. We extend the class of covers to which this construction may be applied and study the functoriality of the construction. The major result is that every right inverse of the forgetful functor Qut--->Top is obtainable by the extended Fletcher construction. In Chapter 3 we characterize pairwise zero dimensional bitopological spaces as those admitting transitive quasi-uniformities. An initiality characterization of pairwise zero dimensional bitopological spaces suggested by Brümmer leads to a description of the coarsest right inverse of the forgetful functor. In Chapter 4 we discuss countably based transitive quasi-uniformities, in that they relate to quasi-metrization. We elaborate on a result of Fletcher and Lindgren (1972) and obtain a bitopological analogue. In Chapter 5 we bring together a number of topics which relate to our previous chapters and point to further questions. 2016-03-28T14:25:35Z 2016-03-28T14:25:35Z 1974 Master Thesis Masters MSc http://hdl.handle.net/11427/18241 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Topology Halpin, Michael Norman Transitive quasi-uniform spaces |
| thesis_degree_str | Master's |
| title | Transitive quasi-uniform spaces |
| title_full | Transitive quasi-uniform spaces |
| title_fullStr | Transitive quasi-uniform spaces |
| title_full_unstemmed | Transitive quasi-uniform spaces |
| title_short | Transitive quasi-uniform spaces |
| title_sort | transitive quasi uniform spaces |
| topic | Mathematics Topology |
| url | http://hdl.handle.net/11427/18241 |
| work_keys_str_mv | AT halpinmichaelnorman transitivequasiuniformspaces |