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The Scientific World Journal
Volume 2014, Article ID 123762, 5 pages
http://dx.doi.org/10.1155/2014/123762
Research Article

Countably -Approximating Posets

1College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2Department of Mathematics, Yangzhou University, Yangzhou 225002, China

Received 17 May 2014; Accepted 21 July 2014; Published 5 August 2014

Academic Editor: Jianming Zhan

Copyright © 2014 Xuxin Mao and Luoshan Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

As a generalization of countably -approximating posets, the concept of countably QC-approximating posets is introduced. With the countably -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 -approximating and weakly generalized countably approximating; (2) a poset having countably directed joins is generalized countably approximating if and only if the lattice of all -Scott-closed subsets of is weakly generalized countably approximating.