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On ideal equal convergence

Presented by: 
M Staniszewski University of Gdansk
Date: 
Friday 28th August 2015 - 13:30 to 14:00
Venue: 
INI Seminar Room 1
Abstract: 
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons