The Darboux property in some families of Baire 1 functions

Rok, strany: 1993, 7 - 14

Denote by $D$ the family of Darboux functions, by $P$ the family of Peek's functions ([D. Peek: Baire functions and their restrictions to special sets, Proc. Amer. Math. Soc. 30 (1971), 303–307]) pointwise discontinuous on each union of sequence of perfect sets, by $G₁$ the family of functions pointwise discontinuous on each nonempty set, and by $Q$ the family of quasicontinuous functions. I investigate the addition and the multiplication in $P$ and $DP$. Moreover, I show that $DP\subset Q$, and that $f\in G₁$ iff for every perfect set $E$ there is an open interval $I$ such that $I\cap E≠\emptyset$ and $f|(I\cap E)$ is continuous.

ISO 690:

Grande, Z. 1993. The Darboux property in some families of Baire 1 functions. In Tatra Mountains Mathematical Publications, vol. 2, no.1, pp. 7-14. 1210-3195.

APA:

Grande, Z. (1993). The Darboux property in some families of Baire 1 functions. Tatra Mountains Mathematical Publications, 2(1), 7-14. 1210-3195.