We define a metric $d_S$, called the shape metric, on the hyperspace $2^X$ of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyhedra in the shape metric. This fact is applied to show that the hyperspace $(2^ℝ^2}, d_S)$ is separable. On the other hand, we give an example showing that $2^ℝ^2}$ is not separable in the fundamental metric introduced by Borsuk.
4
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW