Ultrafilters and compactification

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

Grantor dc:publisher.institution

University of the Western Cape

Year dc:date.issued

2020

Author dc:creator

• Nxumalo, Mbekezeli Sibahle

• Ultrafilter space
• Compactification
• Reflection
• Monad
• Stable compactification

Licence

• https://uwcscholar.uwc.ac.za/bitstreams/91181122-1f4a-41ba-8714-1c6a24e92770/download