Abstract
In this note, we continue the investigation of the new version of characterized subgroups of the circle group T, namely, “statistically characterized subgroups” (shortly, “s-characterized subgroups”) recently introduced in [12]. We primarily investigate these subgroups for sequences arising out of continued fraction representation of irrational numbers α in line of [22] and [20] (followed by [3–5]) comparing their main results for this new notion and show that these Borel subgroups are strictly larger in size (so nontrivial) than the corresponding characterized subgroups, always having cardinality c and containing the subgroup 〈α〉 and in the process answer the Open Question 6.4 [12] which had asked about the size of the s-characterized subgroup for the celebrated Fibonacci sequence.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
