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TitleUltrafilters and Compactification
AuthorNxumalo, Mbekezeli Sibahle
SubjectUltra filter space
SubjectCompactification
SubjectReflection
SubjectMonad
SubjectStable Compactifi cation
SubjectStone- Cech
SubjectCompactification
Date2020-10-23T08:49:51Z
Date2020-10-23T08:49:51Z
Date2020
Abstract>Magister Scientiae - MSc
AbstractIn 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
PublisherUWC
Identifierhttp://hdl.handle.net/11394/7374