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QFS-Domains and their Lawson Compactness

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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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Authors and Affiliations

  1. Department of Mathematics, Yangzhou University, Yangzhou, 225002, China

    Gaolin Li & Luoshan Xu

  2. Department of Mathematics, Yancheng Teachers College, Yancheng, 224002, China

    Gaolin Li

Authors
  1. Gaolin Li
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  2. Luoshan Xu
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Correspondence to Luoshan Xu.

Additional information

Supported by the NSF of China (61074129, 61103018, 11101352) and the NSF of Jiangsu province of China (BK2010313, BK2011442).

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Li, G., Xu, L. QFS-Domains and their Lawson Compactness. Order 30, 233–248 (2013). https://doi.org/10.1007/s11083-011-9238-9

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  • DOI: https://doi.org/10.1007/s11083-011-9238-9

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