Asymptotic properties of the (convex) hyperspaces

Abstract

It is known that the hyperspaces of compact sets and compact convex set of the Euclidean space $\mathbb R^n$, $n\ge2$, both are homeomorphic to the puctured Hilbert cube. The main result of this note states that these hyperspaces are not coarsely equivalent.

Keywords

• hyperspace, convex set, coarse equivalence