{"id":{"repo_id":"western-cape","oai_identifier":"oai:uwcscholar.uwc.ac.za:10566/22458"},"canonical_url":"https://search.dev.ndltd.org/etd/western-cape/oai:uwcscholar.uwc.ac.za:10566/22458","repository":{"repo_id":"western-cape","name":"University of the Western Cape","base_url":"https://uwcscholar.uwc.ac.za:8443/server/oai/request"},"display":{"title":"Ultrafilters and compactification","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","abstract_html":"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. 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