The Covering Principle for Darboux Baire 1 functions

Piotr Szuca. "The Covering Principle for Darboux Baire 1 functions." Fundamenta Mathematicae 193.2 (2007): 133-140. <http://eudml.org/doc/286423>.

@article{PiotrSzuca2007,
abstract = {We show that the Covering Principle known for continuous maps of the real line also holds for functions whose graph is a connected $G_\{δ\}$ 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)].},
author = {Piotr Szuca},
journal = {Fundamenta Mathematicae},
keywords = {connectivity functions; Darboux functions; Borel measurable functions; Itinerary Lemma; sequences of intervals; -limit sets; attractors; -cover},
language = {eng},
number = {2},
pages = {133-140},
title = {The Covering Principle for Darboux Baire 1 functions},
url = {http://eudml.org/doc/286423},
volume = {193},
year = {2007},
}

TY - JOUR
AU - Piotr Szuca
TI - The Covering Principle for Darboux Baire 1 functions
JO - Fundamenta Mathematicae
PY - 2007
VL - 193
IS - 2
SP - 133
EP - 140
AB - We show that the Covering Principle known for continuous maps of the real line also holds for functions whose graph is a connected $G_{δ}$ 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)].
LA - eng
KW - connectivity functions; Darboux functions; Borel measurable functions; Itinerary Lemma; sequences of intervals; -limit sets; attractors; -cover
UR - http://eudml.org/doc/286423
ER -