Geodesic
The Covering Principle for Darboux Baire 1 functions
Piotr Szuca1
1 Department of Mathematics Gdańsk University Wita Stwosza 57 80-952 Gdańsk, Poland
Fundamenta Mathematicae, Tome 193 (2007) no. 2, pp. 133-140.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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)].
DOI : 10.4064/fm193-2-2
Keywords: covering principle known continuous maps real line holds functions whose graph connected delta subset plane application example approximately continuous hence darboux baire nbsp function closed subset translated become omega limit set solves problem posed bruckner ceder pearson real anal exchange

Piotr Szuca 1

1 Department of Mathematics Gdańsk University Wita Stwosza 57 80-952 Gdańsk, Poland 
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Piotr Szuca. The Covering Principle for Darboux Baire 1 functions. Fundamenta Mathematicae, Tome 193 (2007) no. 2, pp. 133-140. doi : 10.4064/fm193-2-2. http://geodesic.mathdoc.fr/articles/10.4064/fm193-2-2/

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