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2021 SPACES NOT DISTINGUISHING IDEAL CONVERGENCES OF REAL-VALUED FUNCTIONS, II
Miroslav Repický
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Real Anal. Exchange 46(2): 395-422 (2021). DOI: 10.14321/realanalexch.46.2.0395

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 IJ and none(w(I,JQN)-space)=b for every ideal I below J in the Katĕtov partial quasi-ordering of ideals.

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Miroslav Repický. "SPACES NOT DISTINGUISHING IDEAL CONVERGENCES OF REAL-VALUED FUNCTIONS, II." Real Anal. Exchange 46 (2) 395 - 422, 2021. https://doi.org/10.14321/realanalexch.46.2.0395

Information

Published: 2021
First available in Project Euclid: 8 November 2021

Digital Object Identifier: 10.14321/realanalexch.46.2.0395

Subjects:
Primary: 03E17
Secondary: 26A03 , 40A30 , 40A35 , 54A20 , 54G15

Keywords: (I,JQN)-space , (J,K)-equal convergence , capacitous ideal on ω , capacity on ω , cardinal invariants , I-convergence , JKQN-convergence , w(I,JQN)-space

Rights: Copyright © 2021 Michigan State University Press

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Vol.46 • No. 2 • 2021
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