作 者: ;
机构地区: 北京师范大学数学科学学院
出 处: 《北京师范大学学报(自然科学版)》 1984年第2期19-34,共16页
摘 要: 利用随机集研究模糊落影时,需要将可测结构从论域向其幂上提升。与此相联系,需要将拓扑结构从论域向幂上提升。各种结构的提升是模糊数学研究中十分基础的理论课题。已有的超空间理论不能完全满足现在的需要。 In this paper,the author gives some axiomatical descriptions on the neighborhood structures and convergence relations of lattice topology,and proves that they are equivalent descriptions about lattice topology.By means of these results,the author gives a systematic treatment on the theory of hyperspaces from the viewpoint of lattice topology,and presents eight kinds of hypertopologies.Most of the main classical hypertopologies,such as Vieto- ris topology,Myope topology,κ topology,λ topology,are included herein,and some new kinds of hypertopologies are useful for the study of random sets and fuzzy sets.Finally,the author gives some reviews on the fuzzy topo- logy.