作为半连续格的推广,引入了拟半连续格的概念。讨论了拟半连续格的基本性质。在拟半连续格上得到了类似于拟连续偏序集的一些主要结果。同时探讨了半连续格、拟半连续格、交半连续格、交连续格、强连续格几种不同结构之间的关系。最后,讨论了半连续函数空间仍是半连续格的条件。
As a generalization of semicontinuous lattices, the quasi-semicontinuous lattice is introduced and its some basic properties are investigated. The main results of the theory of semicontinuous lattices are carried to quasi-semicontinuous lattices. Moreover, the relation among quasi-semcontinuous lattices, meetcontinuous lattices, meet-semicontinuous lattices, semicontinuous lattices and strongly continuous lattices is studied. Finally the conditions under which the function space of semicontinuous lattices is semicontinuous are discussed.