SPACES NOT DISTINGUISHING IDEAL CONVERGENCES OF REAL-VALUED FUNCTIONS

Abstract

We introduce an alternative definition of the concept of an ideal weak QN-space and compare it with the definition introduced by Bukovský, Das, and Šupina. We classify the properties of spaces expressing some kinds of indistinguishability for various pairs of ideal convergences and semi-convergences. We give combinatorial characterizations of the least cardinalities of spaces not having a particular property and show that they are invariant for classes of spaces that contain metric spaces and are closed under homeomorphisms. The counterexamples proving this are subsets of the Baire space ${}^{\omega }\omega$.