Compactness and Separability of S-topology on Complete Lattice

This paper introduces Scott topology into complete lattice,studies some basic properties of S-topology and discusses the relation between S-topology and Scott topology and Lawson topology.Based the above-mentioned,the paper proves that S-topology on a continuous lattice L is monotone Hausdorff zero-dimensional normal space,which is a sober space,locally compact but not compact in general.