Comparison of some subfamilies of functions having the Baire property

Abstract

We prove that the family$\mathcal {Q}$ of quasi-continuous functions is a strongly porous set in
the space $\mathcal{B}a$ of functions having the Baire property. Moreover, the family $\mathcal{DQ}$ of all
Darboux quasi-continuous functions is a strongly porous set in the space $\mathcal{DB}a$ of Darboux
functions having the Baire property. It implies that each family of all functions having
the $\mathcal{A}$-Darboux property is strongly porous in $\mathcal{DB}a$, if ${A}$ has the (\ast{*})-property .