The concepts of local quasi-bases and dense family on directed complete posets are introduced, and the character and density of a quasicontinuous Domain are defined. Using local quasi-bases, a new equivalent characterization of quasicontinuous Domain is obtained. Relations between the character and the density of a quasicontinuous Domain and those on the related spaces with Scott topology or Lawson topology are discussed. It proved that the character and density of a quasicontinuous Domain are respectively equal to those on the related space with Scott topology, but they are respectively less than or equal to those on the related space with Lawson topology.

quasicontinuous Domain; local quasi-base; density; Scott topology; Lawson topology