摘要
It is discussed in this paper that under what conditions, for a continuous domain L, there is a Scott continuous self-mapping f ： L → L such that the set of fixed points fix（f） is not continuous in the ordering induced by L. For any algebraic domain L with a countable base and a smallest element, the problem presented by Huth is partially solved. Also, an example is given and shows that there is a bounded complete domain L such that for any Scott continuous stable self-mapping f, fix（f） is not the retract of L.
It is discussed in this paper that under what conditions, for a continuous domain L, there is a Scott continuous self-mapping f ： L → L such that the set of fixed points fix（f） is not continuous in the ordering induced by L. For any algebraic domain L with a countable base and a smallest element, the problem presented by Huth is partially solved. Also, an example is given and shows that there is a bounded complete domain L such that for any Scott continuous stable self-mapping f, fix（f） is not the retract of L.
作者
Xiao Yong XI1,2,Yong Ming LI3 1.College of Mathematics and Information Science,Shaanxi Normal University,Shaanxi 710062,P.R.China
2.College of Mathematics Science,Xuzhou Normal University,Jiangsu 221009,P.R.China
3.College of Computer Science,Shaanxi Normal University,Shaanxi 710062,P.R.China
基金
Supported by the National Natural Science Foundation of China (Grant No.10571112)
the National Key Project of Fundamental Research (Grant No.2002CB312200)
