A categorical study of compactness via closure
Date
2009-03
Authors
Van Coller, Henry
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : Stellenbosch University
Abstract
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.
Description
Thesis (MSc (Mathemathical Sciences))--Stellenbosch University, 2009.
Keywords
Compactness, Closure, Kuratowski-Mrowka theorem, Theses -- Mathematics, Dissertations -- Mathematics, Theses -- Applied mathematics, Dissertations -- Applied mathematics