@Article{Ivanova2014,
author = "Ivanova, Gertruda and Wagner-Bojakowska, Elżbieta",
title = "On some subclasses of the family of Darboux Baire 1 functions",
journal = "Opuscula Math.",
year = "2014",
volume = "34",
number = "4",
pages = "777--788",
doi = "http://dx.doi.org/10.7494/OpMath.2014.34.4.777",
url = "http://dx.doi.org/10.7494/OpMath.2014.34.4.777",
abstract = "We introduce a subclass of the family of Darboux Baire 1 functions \(f:\mathbb{R}\rightarrow\mathbb{R}\) modifying the Darboux property analogously as it was done by Z. Grande in [On a subclass of the family of Darboux functions, Colloq. Math. 17 (2009), 95-104], and replacing approximate continuity with \(\mathcal{I}\)-approximate continuity, i.e. continuity with respect to the \(\mathcal{I}\)-density topology. We prove that the family of all Darboux quasi-continuous functions from the first Baire class is a strongly porous set in the space \(\mathcal{DB}_1\) of Darboux Baire 1 functions, equipped with the supremum metric.",
keywords = "Darboux property, strong Świątkowski property, Baire property, \(\mathcal{I}\)-approximate continuity, quasi-continuity",
issn = "1232-9274"
}