Movability relative to various classes of spaces

This article is in answer to a question posed by K. Borsuk [1]. There exists a locally connected continuum $X$ which is movable relative to the class of all spheres, but which is not 2-movable. We shall prove that the classes $\EuScript K$ of movable compacta coincide for the following $\EuScript K$: 1) all polyhedra of dimension $\le n$, 2) all compacta of dimension $\le n$, and 3) gall compacta of fundamental dimension $\le n$. We shall also prove that the movability of a compactum $X$ is equivalent to its movability relative to the class of all polyhedra.