The dimension of hyperspaces of non-metrizable continua
Volume 128 / 2012
Colloquium Mathematicum 128 (2012), 101-107
MSC: Primary 54F45; Secondary 03C98, 54B20.
DOI: 10.4064/cm128-1-9
Abstract
We prove that, for any Hausdorff continuum $X$, if $\dim X \geq 2$ then the hyperspace $C(X)$ of subcontinua of $X$ is not a $C$-space; if $\dim X=1$ and $X$ is hereditarily indecomposable then either $\dim C(X)=2$ or $C(X)$ is not a $C$-space. This generalizes some results known for metric continua.
