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Ideal quasi-normal convergence and related notions

Volume 146 / 2017

Lev Bukovský, Pratulananda Das, Jaroslav Šupina Colloquium Mathematicum 146 (2017), 265-281 MSC: Primary 40A35, 54G15; Secondary 26A03, 54A20. DOI: 10.4064/cm6520-3-2016 Published online: 9 November 2016

Abstract

Recently the second author and D. Chandra (2013) began to study the notion of ideal quasi-normal convergence and some topological notions defined by this convergence. We show how some properties of those notions depend on the ideal; sometimes, they are also equivalent to some property of the ideal. Moreover, we exhibit non-trivial cases when the new notion introduced by the ideal quasi-normal convergence is equivalent to the corresponding original notions. Some relations between the new notions for different ideals are investigated as well. Then we extend the characterization of some of the notions by convergence properties of the topological space ${\rm C}_p({X})$. Finally, we study the relation of the new convergences to the covering properties of the underlying topological space.

Authors

  • Lev BukovskýInstitute of Mathematics
    Faculty of Sciences
    P. J. Šafárik University
    Jesenná 5
    040 01 Košice, Slovakia
    e-mail
  • Pratulananda DasDepartment of Mathematics
    Jadavpur University
    Jadavpur, Kolkata–32, West Bengal, India
    e-mail
  • Jaroslav ŠupinaInstitute of Mathematics
    Faculty of Sciences
    P. J. Šafárik University
    Jesenná 5
    040 01 Košice, Slovakia
    e-mail

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