Article

Separating sets by Darboux Baire 1 and approximately continuous functions

Published in: Quaestiones Mathematicae
Volume 41 , issue 2 , 2018 , pages: 165–171

DOI: 10.2989/16073606.2017.1375043

Author(s): Marcin Szyszkowski WSB University, Poland

Keywords: 26A15 , 26A21 , 54C08 , 03E15 , 54H05 , 26A15 , 26A21 , 54C08 , 03E15 , 54H05

Abstract

We characterize sets A₀, A₁ for which there is a DB1 function f with [f = 0] = A₀ and [f = 1] = A₁. This characterization is a conjunction of necessary conditions for Darboux and for Baire 1 functions. We also characterize sets A⁻, A⁺ for which there is a DB₁ function with [f < 0] = A⁻ and [f > 0] = A⁺. The same characterzations are provided for approximately continuous functions.

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