# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## The Covering Principle for Darboux Baire 1 functions

### Tom 193 / 2007

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

#### Streszczenie

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)].