title: Countably QC-approximating posets.
abstract: As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σc (L)(op) of all σ-Scott-closed subsets of L is weakly generalized countably approximating.
authors.affiliation: College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
authors.forename: Xuxin
authors.initials: X
authors.lastname: Mao
authors.affiliation: Department of Mathematics, Yangzhou University, Yangzhou 225002, China.
authors.forename: Luoshan
authors.initials: L
authors.lastname: Xu
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D011381:Programming Languages; D012660:Semantics