格值Scott连续映射与Scott诱导L-拓扑(Ⅱ)

Lattice-valued Scott Continuous Mappings and Scott Induced L-topologies Ⅱ

本文得到了连续格.超连续格和完全分配格的一组代数刻划和一组拓扑式刻划,对连续格和完全分配格的次直积表示定理的经典证明给出了一个简洁的直接处理,并在更广的框架下建立了一种相当完善的诱导空间理论——Scoot诱导空间理论,表明格值Scott连续映射可在连续格理论、经典格论、一般拓扑学和L-不分明拓扑学之间提供一个重要的连结物.

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.