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Compactness in Groups of Group-Valued Mappings

Author

Listed:
  • Diana Caponetti

    (Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy)

  • Alessandro Trombetta

    (Department of Mathematics and Computer Science, University of Calabria, Ponte Pietro Bucci 31B, 87036 Rende, Italy)

  • Giulio Trombetta

    (Department of Mathematics and Computer Science, University of Calabria, Ponte Pietro Bucci 31B, 87036 Rende, Italy)

Abstract

We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness in such a contest. Our results extend and encompass some generalizations of Fréchet–Šmulian and Ascoli–Arzelà compactness criteria found in the literature.

Suggested Citation

  • Diana Caponetti & Alessandro Trombetta & Giulio Trombetta, 2022. "Compactness in Groups of Group-Valued Mappings," Mathematics, MDPI, vol. 10(21), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3973-:d:953678
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