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Semi-Continuity of Strong Homology Groups of Continuous Maps

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Abstract

In his preprint Strong homology group of continuous map, A. Beridze defined the strong homology groups \( {\overline{\mathrm{H}}}_{\ast } \) of continuous map f : X → Y of compact metric spaces. Our aim is to show that for these groups, there exist the Milnor short exact sequence. Using the obtained result, we prove that there exists a continuous map with trivial Čech homology groups and nontrivial strong homology groups.

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Authors and Affiliations

  1. Shota Rustaveli State University, Batumi, Georgia

    A. Beridze

  2. Shota Rustaveli State University, Batumi, Georgia

    L. Turmanidze

Authors
  1. A. Beridze
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  2. L. Turmanidze
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Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. Algebra and Topology, 91, 2014.

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Beridze, A., Turmanidze, L. Semi-Continuity of Strong Homology Groups of Continuous Maps. J Math Sci 211, 13–30 (2015). https://doi.org/10.1007/s10958-015-2599-7

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  • DOI: https://doi.org/10.1007/s10958-015-2599-7

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