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Movability relative to various classes of spaces

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Abstract

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

of movable compacta coincide for the following

: 1) all polyhedra of dimension ⩽n, 2) all compacta of dimension ⩽n, and 3) all compacta of fundamental dimension ⩽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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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    S. A. Bogatyi & V. A. Kalinin

Authors
  1. S. A. Bogatyi
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  2. V. A. Kalinin
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Additional information

Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 125–132, January, 1977.

The authors would like to thank Yu. M. Smirnov for the great interest he showed in this article.

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Bogatyi, S.A., Kalinin, V.A. Movability relative to various classes of spaces. Mathematical Notes of the Academy of Sciences of the USSR 21, 68–71 (1977). https://doi.org/10.1007/BF02317040

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  • DOI: https://doi.org/10.1007/BF02317040

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