ON FUNCTIONS HAVING THE PROPERTY OF BAIRE

Abstract

By replacing the $\sigma$-ideal of meager sets with an arbitrary $\mathcal{I}$ ideal of codense sets, a theorem of $\text{M}$. Wilhelm is generalized. In particular, it is shown that every function $f:X\to Y$ that is almost continuous (with respect to $\mathcal{I}$) and which has the property of Baire (with respect to $\mathcal{I}$) is $\theta$-continuous.