Recently, several topological properties of inverse limits of compacta with upper semicontinuous set-valued functions have been studied by many authors. The study of such inverse limits has developed into one of rich topics of geometric topology. ...
We prove that for each n >= 1 the set of all surjective continuum-wise injective maps from an n-dimensional continuum onto an LCn-1-continuum with the disjoint (n-1, n)-cells property is a dense G(delta)-subset of the space of all surjective maps....
TOPOLOGY AND ITS APPLICATIONS 196(A) 54-59 2015年12月 [査読有り]
In this note, we study some dynamical decomposition theorems of spaces related to given homeomorphisms. First, we prove that if f : X -> X is a homeomorphism of an n-dimensional separable metric space X with zero-dimensional set of periodic points...
Colorings for set-valued maps
Scientiae Mathematicae Japonicae 2016年 [査読有り]
Dynamical decomposition theorems (Set-theoretic/geometric topology and related topics)
平木, 正俊; 加藤, 久男
数理解析研究所講究録 1932 21-24 2015年1月
Function spaces and isometrical extensions of bounded isometries of separable metric spaces
数理解析研究所講究録 1884 107-111 2015年
On isometrical extension properties of function spaces
In this note, we investigate metric compactifications preserving some properties of periodic points of maps. In particular, we prove that if f : X -> X is any map of a locally compact and finite-dimensional separable metric space X, then there exi...