## Alejandro Illanes

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

Comment.Math.Univ.Carolin. 57,1 (2016) 97-101.**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

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