Linear extensions of Baire-one and Borel functions

2023/12/05 by Sieg, Waldemar
#54C20 #54C30 #FOS: Mathematics #General Topology (math.GN) #Primary: 26A15 #Secondary: 26A21

paper · doi:10.48550/arxiv.2312.03765

Abstract

Let X and Y be the Hausdorff topological spaces and let A be both an \fs- and \gd- subset of X. Let also f\cn A→ Y be a function for which the inverse image of every open subset U⊂ Y is \fs in X. We show that f can be linearly extended to a function with the same property defined on X. A similar result is proved for Baire-one function defined on an analogous subset of \mR. We give also an answer when the extension map is (with a supremum norm) an isometry.

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