On coarse equivalence of the hyperspaces of euclidean spaces

Анотація

We prove that the hyperspace and the hyperspace of continua of the euclidean space ${\mathrm{ℝ}}^n$ are not coarsely equivalent. Also, we show that the hyperspace of continua in ${\mathrm{ℝ}}^n$, $n\ge 2$, is not geodesic.