2020/11/07 by Pratulananda Das, Das, Pratulananda, Kumardipta Bose +1
Mathematics · #11J70 #22B05 #FOS: Mathematics #General Topology (math.GN) #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2011.03786
openalex publication_date 2020/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we continue the investigation of the new version of characterized subgroups of the circle group \mathbbT, namely, "statistically characterized subgroups" (shortly, "s-characterized subgroups") recently introduced in \citeDDB. We primarily investigate these subgroups for sequences arising out of continued fraction representation of irrational numbers α in line of \citeL and \citeKL (followed by \citeBDMW1) comparing their main results for this new notion and show that these subgroups are strictly larger in size (so nontrivial) than the corresponding characterized subgroups, having cardinality \mathfrakc and containing the subgroup ⟨ α⟩ and in the process answer the Open Question 6.4 posed in \citeDDB.