Choice-Free Dualities for Domains |
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Authors: | Marcel Erné |
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Institution: | 1.Faculty for Mathematics and Physics,Leibniz University,Hannover,Germany |
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Abstract: | A basic tool in domain theory and point-free topology are (Scott) open filters in a partially ordered set. A systematic investigation of that concept shows that central notions and facts like Lawson’s famous self-duality of the category of continuous domains may be established without invoking any choice principles, if only continuous domains are replaced by so-called δ-domains, which coincide with the former in the presence of dependent choices. Many of the conclusions remain valid for the more flexible notion of ζ-domains, comprising important variants such as algebraic or hypercontinuous domains. |
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