Birkhoff's order-convergence in partially ordered sets

作者:Sun, Tao; Li, Qingguo*; Guo, Lankun
来源:Topology and Its Applications, 2016, 207: 156-166.
DOI:10.1016/j.topol.2016.05.001

摘要

By introducing new approximation relations on posets, the notion of S* -doubly continuous posets is proposed and its relationship with doubly continuous posets is presented. Aslo the B-topology on posets is defined and the special properties of the B-topology on S* -doubly continuous posets are studied. Then, a sufficient and necessary condition for the Birkhoff's order-convergence in a poset being topological is obtained.