CARDINAL INVARIANTS CONCERNING FUNCTIONS WHOSE PRODUCT IS ALMOST CONTINUOUS

Abstract

We prove that the smallest cardinality of a family $\mathcal{F}$ of real functions for which there is no non-zero function $g:ℝ\to ℝ$ with the property that $f\cdot g$ is almost continuous (connected, Darboux function, respectively) for all $f\in \mathcal{F}$, is equal to the cofinality of the continuum.