Spaces not distinguishing ideal convergences of real-valued functions. II (Q2054578)

This paper concerns sequences of real-valued functions on a space \(X\) that converge in various weak senses, particularly \(I\)-converging and \(I\)QN-converging sequences where \(I\) is some ideal on \(\omega\), and some weakenings of these involving the Katĕtov order. From each pair of these various notions of convergence arises a topological property of the space \(X\): the property that every sequence in \(X\) converging in one sense also converges in another sense. In other words, the author is interested in topological properties expressing the indistinguishability of various pairs of ideal (semi-)convergences. This paper, following up on the investigation begun in its predecessor, focuses on three classes of such indistinguishability properties, each class being a collection of properties parametrized by an ideal (or two). Associated to each of these properties is a cardinal invariant, namely the least size of a space not having the property. The main results relate these cardinal invariants to the unbounding number \(\mathfrak{b}\), showing that for some ideals the cardinal in question is bounded above by \(\mathfrak{b}\), and for other ideals that it is equal to \(\mathfrak{b}\). For Part I see [the author, ibid. 46, No. 2, 367--394 (2021; Zbl 1489.03013)].