QFS-Domains and their Lawson Compactness |
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Authors: | Gaolin Li Luoshan Xu |
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Affiliation: | 1. Department of Mathematics, Yangzhou University, Yangzhou, 225002, China 2. Department of Mathematics, Yancheng Teachers College, Yancheng, 224002, China
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Abstract: | In this paper, concepts of quasi-finitely separating maps and quasi-approximate identities are introduced. Based on these concepts, QFS-domains and quasicontinuous maps are defined. Properties and characterizations of QFS-domains are explored. Main results are: (1) finite products, nonempty Scott closed subsets and quasicontinuous projection images of QFS-domains, as well as FS-domains, are all QFS-domains; (2) QFS-domains are compact in the Lawson topology; (3) An L-domain is a QFS-domain iff it is an FS-domain, iff it is compact in the Lawson topology; (4) Bounded complete quasicontinuous domains, in particular quasicontinuous lattices, are all QFS-domains. |
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