Abstract

For a continuous poset P, let ω(P) and λ(P) be the lower topology and the Lawson topology on P, respectively. In this paper, we constructively prove in the set theory ZFDC ω (the theory obtained by adjoining the axiom of ω dependent choices to the Zermelo–Fraenkel set theory) that if all lower closed subsets in (P,λ(P)) are closed in (P,ω(P)), then (P,λ(P)) is a strictly completely regular ordered space.

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