Statistically characterized subgroups of the circle

Dikran Dikranjan, Pratulananda Das, Kumardipta Bose Fundamenta Mathematicae MSC: Primary 22B05; Secondary 11B05, 40A05. DOI: 10.4064/fm690-8-2019 Published online: 13 December 2019

Abstract

In this paper, we introduce a new version of characterized subgroups of the circle group $\mathbb T $ that we call statistically characterized subgroups (briefly, s-characterized subgroups). We primarily investigate these subgroups for arithmetic sequences of integers and show that these subgroups are essentially different and strictly larger in size than the much investigated class of characterized subgroups, having cardinality $\mathfrak {c}$ but remaining nontrivial (i.e. different from $\mathbb T $) though remaining topologically nice.

Authors

  • Dikran DikranjanDepartment of Mathematics
    Udine University
    Via delle Scienze 206
    Udine 33100, Italy
    e-mail
  • Pratulananda DasDepartment of Mathematics
    Jadavpur University
    Kolkata-700032, India
    e-mail
  • Kumardipta BoseDepartment of Mathematics
    Jadavpur University
    Kolkata-700032, India
    e-mail

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