Formal topological characterizations of various continuous domains

Authors:
Luoshan Xu;Xuxin Mao
Affiliations:
Department of Mathematics, Yangzhou University, Yangzhou 225002, PR China;College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this paper, some new concepts such as (super-compact) quasi-bases and the consistently (locally) coherent property of super-compact quasi-bases, are introduced. With these concepts, various continuous domains including bc-domains and (s)L-domains, are successfully characterized in formal topological ways. Furthermore, to deal with algebraic domains, the concept of quasi-formal points, a generalization of formal points, is introduced. Formal topological characterizations of various algebraic domains via quasi-formal points are obtained.