A categorical study of compactness via closure

Van Coller, Henry (2009-03)

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/2351
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