We show that the Covering Principle known for continuous maps of the real line also holds for functions whose graph is a connected subset of the plane. As an application we find an example of an approximately continuous (hence Darboux Baire 1) function f: [0,1] → [0,1] such that any closed subset of [0,1] can be translated so as to become an ω-limit set of f. This solves a problem posed by Bruckner, Ceder and Pearson [Real Anal. Exchange 15 (1989/90)].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-2,
author = {Piotr Szuca},
title = {The Covering Principle for Darboux Baire 1 functions},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {133-140},
zbl = {1123.26003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-2}
}
Piotr Szuca. The Covering Principle for Darboux Baire 1 functions. Fundamenta Mathematicae, Tome 193 (2007) pp. 133-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-2/