准连续Domain和稳定映射

Precontinuous domains and stable mappings

研究了准连续Domain的积结构,子结构和商结构.给出了有界完备准连续Domain上同余关系的等价刻画.讨论了有界完备准连续Domain上稳定映射及其相关性质,证明了有界完备准连续Domain上保定向并的映射是稳定映射当且仅当它保非空交,指出了有界完备准连续Do-main上保有限交的映射是稳定映射当且仅当它关于Lawson拓扑连续.

The products, substructures and quotients of precontinuous domains are studied. The congruence on bounded complete precontinuous domains is characterized. It is proved that the map keeping a directed subset＇s sup on bounded complete proecontinuous domains is a stable map if and only if it keeps nonempty subset＇s inf. Furthermore,it is proved that a map keeping finite subset＇s inf on bounded complete precontinuous domains is a stable map if and only if it is continuous with respect to Lawson topology.