>Magister Scientiae - MSc / In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As part of investigating some properties of the ultrafilter space, we show that the ultrafilter space forms a monad in the category of topological spaces. Furthermore, we show that rendering the ultrafilter space suitably separated results in a generation of separated compactifications which coincide with some well-known compactifications. When the ultrafilter space is rendered T0 or sober, the resulting compactifications is a stable Compactifications. Rendering the ultrafilter space T2 or Tychono results in the Stone_ Cechcompactification
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uwc/oai:etd.uwc.ac.za:11394/7374 |
| Date | January 2020 |
| Creators | Nxumalo, Mbekezeli Sibahle |
| Contributors | Raza ndrakoto, Ando |
| Publisher | UWC |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Rights | UWC |
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