Urysohnness on Completely Distributive Lattice
Yan Feng · Mohu xitong yu shuxue · 2003
The primary interest of this paper is the investigation of Urysohn axiom on lattices and the lattice is not required to be with any order-reversing involution. We show that the lattice with property of Urysohn must be Hausdorff and the property of Urysohnness is hereditary. Characterizations of Urysohn are given in terms of filters and nets. These characterizations are obtained mainly through the introduction of a type of convergence for filters and nets that we call L-Urysohn-convergence.