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Covariant Functors and Shapes in Category of Compacta

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Abstract

In this paper, we consider covariant functors F : Comp → Comp acting in category of shape-preserving compact sets [2], infinite compact sets, and shape equivalence [6]. Also we study action of compact functors and shape properties of the compact space X consisting of connected components X of the compact X as well as shape identity ShX = ShY of infinite compacts X and Y for the space P(X) of probability measures and its subspaces.

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Authors and Affiliations

  1. Tashkent State Pedagogical University named after Nizami, Tashkent, Uzbekistan

    T. F. Zhuraev & Z. O. Tursunova

  2. Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Tashkent, Uzbekistan

    K. R. Zhuvonov

Authors
  1. T. F. Zhuraev
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  2. Z. O. Tursunova
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  3. K. R. Zhuvonov
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Corresponding author

Correspondence to T. F. Zhuraev.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 65, No. 1, Contemporary Problems in Mathematics and Physics, 2019.

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Zhuraev, T.F., Tursunova, Z.O. & Zhuvonov, K.R. Covariant Functors and Shapes in Category of Compacta. J Math Sci 265, 21–32 (2022). https://doi.org/10.1007/s10958-022-06041-1

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  • DOI: https://doi.org/10.1007/s10958-022-06041-1

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