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 σ c(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating.
展开▼
机译：作为可数C近似姿态的概括，引入了可数QC近似姿态的概念。通过具有可数的QC逼近性质，给出了广义的完全分布格和广义的可数逼近姿态的一些表征。主要结果如下：（1）当且仅当它是可数QC近似且弱广义可数近似时，一个完全格才是广义完全分布的； （2）当且仅当L的所有σ-斯科特闭合子集的晶格σc（L） op 弱广义地可广义近似时，具有可数定向的连接的球状体L才被近似可广义地近似。
展开▼
