Intrinsic approach spaces on domains |
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Authors: | E Colebunders S De Wachter B Lowen |
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Institution: | a Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium b Department of Mathematics & Informatics, Universiteit Antwerpen, Middelheimlaan 1, 2020 Antwerpen, Belgium |
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Abstract: | The paper is a contribution to quantifiability of domains. We show that every domain X, regardless of cardinality conditions for a domain bases, is quantifiable in the sense that there exists an approach structure on X (Lowen (1997) 9]), defined by means of a gauge of quasi metrics, inducing the Scott topology. We get weightability for free and in the case of an algebraic domain satisfying the Lawson condition (Lawson (1997) 8]), a quantifying approach space can be obtained with a weight satisfying the kernel condition. |
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Keywords: | 06A06 06b35 06F30 54A05 54B30 54E35 |
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