两个空间之间复合映射的不动点集和Reidemeister数

数学物理学报 ›› 2005, Vol. 25 ›› Issue (7): 952-955.

两个空间之间复合映射的不动点集和Reidemeister数

夏大峰, 江波

南京信息工程大学数学系南京 210044

出版日期:2005-12-30 发布日期:2005-12-30
基金资助:
南京气象学院科研基金资助

Set of Fixed Points and Reidemeister Number of Compound Mapping between Tow Spaces

XIA Da-Feng, JIANG Bo

Online:2005-12-30 Published:2005-12-30
Supported by:
南京气象学院科研基金资助

摘要/Abstract

摘要：

设X,Y为拓扑空间,f:X--> Y, g:Y--> X.该文证明了下列结论：对每一自然数n,(1)f(Fix((g f)^n))=Fix((f g)^n), g(Fix((f g)^n))=Fix((g f)^n),且#Fix((g f)^n)=#Fix((f g)^n);(2)R((g f)^n)=R((f g)^n).

关键词: 自映射;不动点集;不动点类;Reidemeister数;拓扑熵

Abstract:

Let X,Y be topological spaces, f:X-->Y,g:Y-->X. In this paper, follow conclutions are obtained:(1)f(Fix((g f)^n))=Fix((f g)^n), g(Fix((f g)^n))=Fix((g f)^n),and #Fix((g f)^n)=#Fix((f g)^n);(2)R((g f)^n)=R((f g)^n).where n is a natural number.

Key words: Self-maps, Set of fixed points, Fixed point class, Reidemeister number; Topological entropy

中图分类号:

夏大峰, 江波. 两个空间之间复合映射的不动点集和Reidemeister数[J]. 数学物理学报, 2005, 25(7): 952-955.

XIA Da-Feng, JIANG Bo. Set of Fixed Points and Reidemeister Number of Compound Mapping between Tow Spaces[J]. Acta mathematica scientia,Series A, 2005, 25(7): 952-955.