Note about Fixed Points of Scott Continuous Self-Mappings  

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 

出　　处：《Journal of Mathematical Research and Exposition》2011年第1期187-190,共4页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10571112);the National Key Project of Fundamental Research (Grant No.2002CB312200)

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.

关 键 词：Scott continuous fixed points stable mapping. 

分 类 号：O189.1[理学—数学] O153.1[理学—基础数学]