On ideal equal convergence

• Autorzy: Rafał Filipów , Marcin Staniszewski
• Języki publikacji: EN

Abstrakty

EN

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 R., Szuca P., Three kinds of convergence and the associated I-Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9]. We also solve a few problems posed in the paper by Das, Dutta and Pal.

Słowa kluczowe

EN

Ideal; P-ideal; Filter; Ideal convergence; Statistical convergence; Filter convergence; -convergence; Convergence of a sequence of functions; Equal convergence; Uniform convergence; Pointwise convergence; Sigma-uniform convergence

Kategorie tematyczne

• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
• 40A30: Convergence and divergence of series and sequences of functions
• 26A03: Foundations: limits and generalizations, elementary topology of the line
• 40A35: Ideal and statistical convergence

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 6
• Strony: 896-910

Daty

wydano

2014-06-01

online

2014-03-19

Twórcy

autor

Rafał Filipów

• University of Gdańsk

autor

Marcin Staniszewski

• University of Gdańsk

Bibliografia

• [1] Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472
• [2] Császár Á., Laczkovich M., Some remarks on discrete Baire classes, Acta Math. Acad. Sci. Hungar., 1979, 33(1–2), 51–70 http://dx.doi.org/10.1007/BF01903381
• [3] Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177
• [4] Filipów R., Szuca P., Three kinds of convergence and the associated -Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9 http://dx.doi.org/10.1016/j.jmaa.2012.02.041
• [5] Hernández-Hernández F., Hrušák M., Cardinal invariants of analytic P-ideals, Canad. J. Math., 2007, 59(3), 575–595 http://dx.doi.org/10.4153/CJM-2007-024-8
• [6] Kostyrko P., Šalát T., Wilczyński W., -convergence, Real Anal. Exchange, 2000/01, 26(2), 669–685
• [7] Mačaj M., Sleziak M., -convergence, Real Anal. Exchange, 2010/11, 36(1), 177–193
• [8] Todorčevic S., Analytic gaps, Fund. Math., 1996, 150(1), 55–66

Identyfikatory

DOI

10.2478/s11533-013-0388-4