Nested ideals and topologically \mathbf u_\mathcal I-torsion elements of the circle group

2025/05/06 by Di santo, R., Dikranjan, D., Bruno, A. Giordano +1
#11J71 #20K45 #22A10 #40A35 #54H11 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2505.03548

Abstract

Let \mathbf u=(u_n)_{n∈\mathbb N} be a sequence in \mathbb N₊ with u₀=1 and u_n| u_n+1 for every n∈\mathbb N, and let b_n:=u_n+1/u_n for every n∈\mathbb N₊. For every r∈ [0,1), there exists a unique sequence (c_n)_{n∈\mathbb N+} in \mathbb N such that r= ∑_n=1^∞(c_n)/(u_n), with c_n

Citations

• Topological torsion elements via natural density and a quest for solution of Armacost like problem

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