Ascoli-Type Theorem for Baire 1 Functions

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

Mathematics, 2023, vol. 11, issue 17, 1-9

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 .

Keywords: Baire 1 function; topology of uniform convergence on compacta; equi-Lebesgue family; compactness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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