Countably QC-Approximating Posets

Abstract EN

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 σcLop of all σ-Scott-closed subsets of L is weakly generalized countably approximating.