格值连续函数和L-Fuzzy紧性

LATTICE-VALUED CONTINUOUS MAPPINGS AND L-FUZZY COMPACTNESS

第一部分研究值域为连续格的一类广泛的格值映射,得到Scott连续函数分析式、层次式刻划,改进了有关结果.第二部分主要研究不分明紧性,用笛卡尔积和闭投射给出了Fuzzy紧性外部刻划定理,将一般拓朴学著名的Kuratowski定理推广到LF拓扑学中,同时给出一种不分明完备映射的一个等价刻划,完善了有关结果.

There are two parts in this paper. In the first part, we obtain the analytic and level characterization of Scott continuous mappings after studying a class of general lattice- valued mappings, which improves the relative results in [1 - 7]. In the second part, a characterization of fuzzy compactness is established in terms of Cartesian products and closed projections, which extends the famous Kuratowski theorem (ef. [8,18]) in general topology. Basing on this result, we give a characterization of fuzzy psrfect mappings, so that we improve the main results in [9] and answer the question in [10].