We introduce some families of functions $f :\mathbb{R} \to \mathbb{R}$modifying Darboux property analogously as it was done by A. Mal-iszewski in [14], changing continuity with $\mathcal{A}$-continuity, i.e. continuity with respect to some family $\mathcal{A}$ of subsets in the domain.We prove that if $\mathcal{A}$ has the $(*)$-property then the family $\mathcal{D_A} offunctions having $\mathcal{A}$-Darboux property is contained and dense inthe family $\mathcal{DQ}$ of Darboux quasi-continuous functions.
@article{268,
title = {On some modification of \'Swi\k atkowski property},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v58i0.268},
language = {EN},
url = {http://dml.mathdoc.fr/item/268}
}
Ivanova, Gertruda; Wagner-Bojakowska, Elżbieta. On some modification of Świątkowski property. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v58i0.268. http://gdmltest.u-ga.fr/item/268/