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On ideal equal convergence

Rafał Filipów, Marcin Staniszewski (2014)

Open Mathematics

We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów...

On the ideal convergence of sequences of quasi-continuous functions

Tomasz Natkaniec, Piotr Szuca (2016)

Fundamenta Mathematicae

For any Borel ideal ℐ we describe the ℐ-Baire system generated by the family of quasi-continuous real-valued functions. We characterize the Borel ideals ℐ for which the ideal and ordinary Baire systems coincide.

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