Properties and Characterizations of Countably C-approximating Posets
Xuxin Mao
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China.
Luoshan Xu *
Department of Mathematics, Yangzhou University, Yangzhou, P.R. China
*Author to whom correspondence should be addressed.
Abstract
In this paper, the concept of countably C-approximating posets is introduced. Properties and characterizations of countably C-approximating posets are presented. Main results are: (1) the lattice of all σ-Scott-closed subsets for any poset is countably C-approximating; (2) a complete lattice is completely distributive iff it is countably approximating and countably C-approximating.
Keywords: σ-Scott topology; countably C-approximating poset, semilattice, principal ideal, completely distributive lattice