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Ascoli-Type Theorem for Baire 1 Functions

Author

Listed:
  • Ľubica Holá

    (Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia)

Abstract

Let X , Y be metric spaces and B 1 ( X , Y ) be the space of Baire 1 functions from X to Y . The main purpose of this paper is to study compact subsets of B 1 ( X , Y ) equipped with the topology τ U C of uniform convergence on compacta and prove Ascoli-type theorem for locally bounded Baire 1 functions. The key notion in our paper is the notion of equi-Lebesgue family of functions from X to Y .

Suggested Citation

  • Ľubica Holá, 2023. "Ascoli-Type Theorem for Baire 1 Functions," Mathematics, MDPI, vol. 11(17), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3694-:d:1226784
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