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Showing 1 to 1 of 1 (0.036 seconds)Spelling suggestions: "subject:"kuratowski theorem"" "subject:"kuratowski’s theorem""
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A categorical study of compactness via closureVan Coller, Henry 03 1900 (has links)
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.
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