The dimension of hyperspaces of non-metrizable continua

Volume 128 / 2012

Wojciech Stadnicki Colloquium Mathematicum 128 (2012), 101-107 MSC: Primary 54F45; Secondary 03C98, 54B20. DOI: 10.4064/cm128-1-9


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.


  • Wojciech StadnickiMathematical Institute
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50–384 Wrocław, Poland

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