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Scott连续自映射不动点的注记
引用本文:奚小勇,李永明.Scott连续自映射不动点的注记[J].数学研究及应用,2011,31(1):187-190.
作者姓名:奚小勇  李永明
作者单位:陕西师范大学数学与信息科学学院, 陕西 西安 710062; 徐州师范大学数学科学学院, 江苏 徐州 221009;陕西师范大学计算机科学学院, 陕西 西安 710062
基金项目:国家自然科学基金(Grant No.10371085); 国家基础研究重点项目(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.

关 键 词:Scott  continuous  fixed  points  stable  mapping.
收稿时间:2008/8/10 0:00:00
修稿时间:2008/9/24 0:00:00

Note about Fixed Points of Scott Continuous Self-Mappings
Xiao Yong XI and Yong Ming LI.Note about Fixed Points of Scott Continuous Self-Mappings[J].Journal of Mathematical Research with Applications,2011,31(1):187-190.
Authors:Xiao Yong XI and Yong Ming LI
Institution:1. College of Mathematics and Information Science,Shaanxi Normal University,Shaanxi710062,P.R.China;College of Mathematics Science,Xuzhou Normal University,Jiangsu 221009,P.R.China
2. College of Computer Science,Shaanxi Normal University,Shaanxi 710062,P.R.China
Abstract:It is discussed in this paper that under what conditions, for a continuous domain $L$, there is a Scott continuous self-mapping $f:L\rightarrow L$ such that the set of fixed points ${\rm fix}(f)$ 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 $f$, ${\rm fix}(f)$ is not the retract of $L$.
Keywords:Scott continuous    fixed points  stable mapping  
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