拟半连续格和交半连续格  

Quasi-semicontinuous Lattices and Meet-semicontinuous Lattices

作　　者：伍秀华[1] 李庆国[2] 

机构地区：[1]中南林业科技大学数学与物理研究所,湖南长沙410004 [2]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《模糊系统与数学》2008年第6期11-16,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10771056);湖南省自然科学基金资助项目(06JJ2004108JJ3132)

摘　　要：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.

关 键 词：〈=-关系 拟半连续格 交半连续格 强半连续映射 函数空间 

分 类 号：O153[理学—数学]