Asymptotic properties of the (convex) hyperspaces - Mykhailo Zarichnyi; Mykhailo Romanskyi (Pracì Mìžnarodnogo Geometričnogo Centru, 2020)
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.