TY  - JOUR
ID  - Ivanova2014
LB  - Ivanova2014
AU  - Ivanova, Gertruda
AU  - Wagner-Bojakowska, Elżbieta
TI  - On some subclasses of the family of Darboux Baire 1 functions
ST  - On some subclasses of the family of Darboux Baire 1 functions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 4
SP  - 777
EP  - 788
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.4.777
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.4.777
AB  - 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.
KW  - Darboux property
KW  - strong Świątkowski property
KW  - Baire property
KW  - \(\mathcal{I}\)-approximate continuity
KW  - quasi-continuity
SN  - 1232-9274
ER  -