TY - JOUR A2 - Zhan, Jianming AU - Mao, Xuxin AU - Xu, Luoshan PY - 2014 DA - 2014/08/05 TI - Countably -Approximating Posets SP - 123762 VL - 2014 AB - 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. SN - 2356-6140 UR - https://doi.org/10.1155/2014/123762 DO - 10.1155/2014/123762 JF - The Scientific World Journal PB - Hindawi Publishing Corporation KW - ER -