dc.contributor.advisor | Raza ndrakoto, Ando | |
dc.contributor.author | Nxumalo, Mbekezeli Sibahle | |
dc.date.accessioned | 2020-10-23T08:49:51Z | |
dc.date.available | 2020-10-23T08:49:51Z | |
dc.date.issued | 2020 | |
dc.identifier.uri | http://hdl.handle.net/11394/7374 | |
dc.description | >Magister Scientiae - MSc | en_US |
dc.description.abstract | 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 | en_US |
dc.language.iso | en | en_US |
dc.publisher | UWC | en_US |
dc.subject | Ultra filter space | en_US |
dc.subject | Compactification | en_US |
dc.subject | Reflection | en_US |
dc.subject | Monad | en_US |
dc.subject | Stable Compactifi cation | en_US |
dc.subject | Stone- Cech | en_US |
dc.subject | Compactification | en_US |
dc.title | Ultrafilters and Compactification | en_US |
dc.rights.holder | UWC | en_US |