On some subclasses of the family of Darboux Baire 1 functions

We introduce a subclass of the family of Darboux Baire 1 functions f : R → 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 I-approximate continuity, i.e. continuity with respect to the 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 DB1 of Darboux Baire 1 functions, equipped with the supremum metric.