We give a sufficient and necessary condition when the ideal pointwise
convergence implies the ideal equal (aka quasi-normal) convergence. The
characterization is expressed in terms of a cardinal coefficient related to the bounding number $\mathfrak{b}$. We examine this coefficient for nice ideals.
I would like also to mention two other ideal versions of the bounding number (one introduced by Farkas an Soukup, and another introduced by Brendle).
Moreover, I would like to present some results about QN-spaces (introduced by Bukovsky-Reclaw-Repicky) and their ideal counterparts.
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