Cells and $n$-fold hyperspaces
Volume 145 / 2016
Colloquium Mathematicum 145 (2016), 157-166
MSC: Primary 54B20.
DOI: 10.4064/cm6527-1-2016
Published online: 25 April 2016
Abstract
We prove that $X$ is a hereditarily indecomposable metric continuum if and only if the $n$-fold hyperspace ${\mathcal C}_n(X)$ does not contain $(n+1)$-cells, for any positive integer $n$. Also we characterize the class of continua whose $n$-fold hyperspaces and $n$-fold hyperspace suspensions are cells.
