The Covering Principle for Darboux Baire 1 functions

Volume 193 / 2007

Piotr Szuca Fundamenta Mathematicae 193 (2007), 133-140 MSC: Primary 26A18; Secondary 26A15, 26A21, 37E05, 54C30. DOI: 10.4064/fm193-2-2


We show that the Covering Principle known for continuous maps of the real line also holds for functions whose graph is a connected $G_\delta $ subset of the plane. As an application we find an example of an approximately continuous (hence Darboux Baire 1) function $f: [0,1]\to [0,1]$ such that any closed subset of $[0,1]$ can be translated so as to become an $\omega $-limit set of $f$. This solves a problem posed by Bruckner, Ceder and Pearson [Real Anal. Exchange 15 (1989/90)].


  • Piotr SzucaDepartment of Mathematics
    Gdańsk University
    Wita Stwosza 57
    80-952 Gdańsk, Poland

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