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2021 SPACES NOT DISTINGUISHING IDEAL CONVERGENCES OF REAL-VALUED FUNCTIONS
Miroslav Repický
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Real Anal. Exchange 46(2): 367-394 (2021). DOI: 10.14321/realanalexch.46.2.0367

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 ωω.

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Miroslav Repický. "SPACES NOT DISTINGUISHING IDEAL CONVERGENCES OF REAL-VALUED FUNCTIONS." Real Anal. Exchange 46 (2) 367 - 394, 2021. https://doi.org/10.14321/realanalexch.46.2.0367

Information

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

Digital Object Identifier: 10.14321/realanalexch.46.2.0367

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

Keywords: (J,K)-equal convergence , cardinal invariants , I-convergence , ideal on ω , JKQN-convergence , QN-space , wQN-space , wβγ-space , βγ-space

Rights: Copyright © 2021 Michigan State University Press

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Vol.46 • No. 2 • 2021
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