A continuum $X$ such that $C(X)$ is not continuously homogeneous

Commentationes mathematicae Universitatis Carolinae

Alejandro Illanes¹ 

关键词: continuum;    continuously homogeneous;    hyperspace;   

DOI  :  10.14712/1213-7243.2015.146

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

A metric continuum $X$ is said to be continuously homogeneous provided that for every two points $p,q\in X$ there exists a continuous surjective function $fX\rightarrow X$ such that $f(p)=q$. Answering a question by W.J.~Charatonik and Z.~Garncarek, in this paper we show a continuum $X$ such that the hyperspace of subcontinua of $X$, $C(X)$, is not continuously homogeneous.

【 授权许可】

CC BY