The Lawson Topology on Quasicontinuous Domains
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For a directed complete poset P, let λ(P) and σ(P) be the lower topology and the Lawson topology on P respectively. We constructively prove that if P is a quasicontinuous domain and all lower closed subsets in (P, λ(P)) are closed in (P, ω(P)),then (P,λ(P)) is strictly completely regular ordered space.
KeywordsQuasicontinuous domain Meet-continuity Lawson topology Strictly complete regularity Hausdorff separation
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