Abstract: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 $f:X\rightarrow X$ 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.
Keywords: continuum; continuously homogeneous; hyperspace
DOI: DOI 10.14712/1213-7243.2015.146
AMS Subject Classification: 54B20 54F15