摘要
本文讨论了半连续格的一些性质,在半连续格中引入半Scott开集族,用半Scott开集族来刻画半连续格,同时定义了半连续格之间的半连续映射,得到闭包算子的像仍是半连续格的条件.最后,研究了半连续格上的半连续映射的全体不动点之集的性质。
In this paper, we mainly discuss some properties of semicontinuous lattices and give the char- acterizations of semicontinuous lattices. We also define functions between two semicontinuous lattices and obtain the conditions under which the image of a closure operator is also semicontinuous. Finally we study the property about fixed points of semicontinuous lattices.
基金
国家自然科学基金(10471035)
教育部博士点基金(2004194).
关键词
半素理想
半连续格
半连续映射
Galois联络
收缩
semiprime ideal
semicontinuous lattice, semicontinuous function, Galois connection
re-tract.
