Strictly complete regularity of the Lawson topology on a continuous poset

✍ Scribed by Xiao-Quan Xu

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 63 KB
• Volume: 103
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00166-7

✦ Synopsis

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.