Generalized Alexandroff Topologies on L-Quasi Ordered Sets
Zheng Chong-you · Mohu xitong yu shuxue · 2002
In this paper,the generalized Alexandroff topology on an L-quasi ordered set is constructed, where L denotes a completely distributive lattice in which 1 is a molecule, it is exactly an Alexandroff topology when restricted to the ordinary quasi ordered set.It is proved that the generalized Alexandroff topology on an L-quasi ordered set (X,e) can be obtained by the join of a family of the Alexandroff topologies on X, and a topology on any topological space can be represented as a generalized Alexandroff topology on an L-quasi ordered set.