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On ideal equal convergence

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Mathematical, Foundational and Computational Aspects of the Higher Infinite

We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Cs’{a}sz’{a}r and Laczkovich. The independent, equivalent definition was introduced by Bukovsk{‘a}. She called it quasi-normal convergence. We study relationships between ideal equal convergence and various kinds of ideal convergences of sequences of real functions.

We prove a characterization showing when the ideal pointwise convergence does not imply the ideal equal (aka quasi-normal) convergence. The characterization is expressed in terms of a cardinal coefficient related to the bounding number. Furthermore we consider ideal version of the bounding number on sets from coideals.

This talk is part of the Isaac Newton Institute Seminar Series series.

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