Geodesic
Movability relative to various classes of spaces
Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 125-132.

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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. 
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     author = {S. A. Bogatyi and V. A. Kalinin},
     title = {Movability relative to various classes of spaces},
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S. A. Bogatyi; V. A. Kalinin. Movability relative to various classes of spaces. Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 125-132. http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a14/