Lattice-valued Scott Continuous Mappings and Scott Induced L-topologies Ⅱ
Xu Xiaoquan(Dept. of Math, of Jiangxi Normal University Nanchang 330027)
In part I ,based on part 1 .a series of algebraic and topological characterizations of continu-ous lattices, hyper-continuous lattices and completely distributive lattices were obtained, and the subdirect-product representation theories for continuous lattices and completely disstributive lattices were set up in a quite different way, which is much simpler and much more direct than the classical ones, and in a more general framework, a satisfactory theory of Scott induced spaces was developed. The work shows that lattice-valued Scott continuous mappings can provide an important link between the following four areas: the theory of continuous lattices,traditional lattice theory, general topology and L-fuzzy topology.