Thesis (MSc (Mathemathical Sciences))--Stellenbosch University, 2009. / We 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/2351 |
| Date | 03 1900 |
| Creators | Van Coller, Henry |
| Contributors | Holgate, David, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | Stellenbosch University |
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