The Covering Principle for Darboux Baire 1 functions
Fundamenta Mathematicae, Tome 193 (2007) no. 2, pp. 133-140
Cet article a éte moissonné depuis 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)].
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
Affiliations des auteurs :
Piotr Szuca 1
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author = {Piotr Szuca},
title = {The {Covering} {Principle} for {Darboux} {Baire} 1 functions},
journal = {Fundamenta Mathematicae},
pages = {133--140},
year = {2007},
volume = {193},
number = {2},
doi = {10.4064/fm193-2-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm193-2-2/}
}
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
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