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Keywords:
continuum; continuously homogeneous; hyperspace
continuum; continuously homogeneous; hyperspace
Summary:
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.
References:
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[5] Illanes A., Nadler S.B., Jr.: Hyperspaces: Fundamentals and Recent Advances. Monographs and Textbooks in Pure and Applied Mathematics, 216, Marcel Dekker, Inc., New York and Basel, 1999. MR 1670250
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