2017
DOI: 10.1016/j.jmaa.2017.01.031
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On ideal equal convergence II

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Cited by 12 publications
(9 citation statements)
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“…The ideal version of quasi-normal convergence has been intensively studied e.g. in [11], [12], [16], [17], [26] and [32].…”
Section: Preliminariesmentioning
confidence: 99%
“…The ideal version of quasi-normal convergence has been intensively studied e.g. in [11], [12], [16], [17], [26] and [32].…”
Section: Preliminariesmentioning
confidence: 99%
“…Then, by Theorem 3.3, |A| < d, a contradiction. Remark 1º ω 1 < b(I) = c, b < b(I) = c, b < d = c and b ≤ b(I) < d = care all consistent with the axioms of (ZFC) (see[10,11,26]). Lemma 3.7, Theorem 3.3, Theorem 3.4, Theorem 3.5 and Theorem 3.6 are summarized in the following figure.…”
mentioning
confidence: 68%
“…In [9], the authors proved that the smallest size of non-QN-space is equal to the bounding number b. The cardinal numbers b(I, J, K) and b s (I, J , K) were introduced by Filip ów and Staniszewski [18,35] to characterize the smallest size of a space which is not ideal-QN. Recently, Repický [31,32] thoroughly examined ideal-QN spaces and, among others, characterized the smallest size of non-ideal-QNspaces in terms of the cardinal b(≥ I ∩(D K × D J )).…”
Section: The Bounding Numbers à La Staniszewskimentioning
confidence: 99%
“…The paper is organized in the following way. In Section 3 we show that b(> I ∩(D K × D J )) = b(I, J , K) and b(≥ I ∩(D K × D J )) = b s (I, J , K), where b(I, J , K) and b s (I, J , K) are cardinals considered by Filip ów and Stanszewski in [18,35]. This provides us with a very useful combinatorial characterizations of the considered cardinals, which we use almost exclusively in the rest of the paper.…”
Section: §1 Introduction For An Ideal I On We Denote D I = {F ∈mentioning
confidence: 99%