Urysohn closedness on completely distributive lattices

The purpose of this paper is to investigate the Urysohn closedness of co-topology on lattices which are not required to have an orderreversing involution. The concept of Urysohn closedness on lattices is introduced and characterizations of Urysohn closedness are given in terms of ideals and nets. These characterizations are obtained mainly through the introduction of a kind of convergence for ideals and nets that we call L-Urysohn convergence.