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A categorical study of compactness via closure

dc.contributor.advisorHolgate, Daviden_ZA
dc.contributor.authorVan Coller, Henryen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
dc.date.accessioned2009-03-06T12:48:54Zen_ZA
dc.date.accessioned2010-06-01T08:46:45Z
dc.date.available2009-03-06T12:48:54Zen_ZA
dc.date.available2010-06-01T08:46:45Z
dc.date.issued2009-03
dc.identifier.urihttp://hdl.handle.net/10019.1/2351en_ZA
dc.descriptionThesis (MSc (Mathemathical Sciences))--Stellenbosch University, 2009.
dc.description.abstractWe have the familiar Kuratowski-Mr owka theorem in topology, where compactness is characterised by a closure and a projection-map (X is compact i p : X Y ! Y is a closed mapping, for any space Y , i.e. p(A) = p(A) A X Y ). Using this as our starting point, we generalise compactness to a categorical setting. We then generalise even further to "asymmetric" compactness. Then we discuss a functional approach to compactness, where we do not explicitly mention closure operators. All this provides economical proofs as well as applications in di erent areas of mathematics.en_ZA
dc.language.isoenen_ZA
dc.publisherStellenbosch : Stellenbosch University
dc.subjectCompactnessen_ZA
dc.subjectClosureen_ZA
dc.subjectKuratowski-Mrowka theoremen_ZA
dc.subjectTheses -- Mathematicsen_ZA
dc.subjectDissertations -- Mathematicsen-ZA
dc.subjectTheses -- Applied mathematicsen_ZA
dc.subjectDissertations -- Applied mathematicsen_ZA
dc.subject.lcshTopologyen_ZA
dc.subject.otherMathematical Sciencesen_ZA
dc.subject.otherMathematicsen_ZA
dc.titleA categorical study of compactness via closureen_ZA
dc.typeThesisen_ZA
dc.rights.holderStellenbosch University


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