Some Researches On Smooth Lattices

In this paper, the basic properties of smooth lattices are discussed. The concepts of strongly smooth lattices, generalized smooth lattices, generalized smooth algebraic lattices and the bases of generalized smooth lattices are introduced. Some mapping properties of theirs are also investigated. And it is proved that strongly smooth lattices can be embedded in [0, 1]~X by a mapping which preserves arbitrary inf and Scott-closed set sup. Finally, some properties and theorems of Z-subset system are discussed. The characterizations of strongly Z-continuous domain and Z-algebraic domain are obtained respectively, the category properties of coreflective of strongly Z-continuous domain and Z- algebraic domain are also discussed.