SPACES NOT DISTINGUISHING IDEAL CONVERGENCES OF REAL-VALUED FUNCTIONS, II

Abstract

In [13] we gave combinatorial characterizations of non(P) of spaces expressing non-distinguishability of some ideal convergences and semi-convergences of sequences of continuous functions. In the present paper we study three of these invariants: non((I,JQN)-space), none((I,≤KJQN)-space), and none(w(I,JQN)-space). We study them in connection with partial orderings of ωω restricted to relations between I-to-one functions and J-to-one functions. In particular we prove that none(w(I,JQN)-space)≤b for every capacitous ideal J on ω. This generalizes the same result of Kwela for ideals J contained in an Fσ-ideal. If J is a capacitous P-ideal, then non((I,JQN)-space)=none((I,≤KJQN)-space)=b for every ideal I⊆J and none(w(I,JQN)-space)=b for every ideal I below J in the Katĕtov partial quasi-ordering of ideals.