A generalisation of the functional approach to compactness |
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Authors: | David Holgate |
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Affiliation: | Department of Mathematical Sciences, University of Stellenbosch, Stellenbosch 7600, South Africa |
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Abstract: | A topological space X is compact iff the projection π:X×Y→Y is closed for any space Y. Taking this as a definition and then asking that π maps α-closed subspaces of X×Y onto β-closed subspaces of Y, for different closures α and β, extends the notion of compactness to include also examples of “asymmetric compactness” pursued in the article.Categorical closure operators and a so-called “functional approach to general topology” are employed to define and prove fundamental properties of compact objects and proper maps in this generalised setting. |
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Keywords: | 18A20 18B30 54A05 54C10 54D20 54D30 |
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