Bounded sequences having an even number of accumulation points

2025/11/11 by Audrey Fovelle, Fovelle, Audrey, Juan B. Seoane‐Sepúlveda +1
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Meromorphic and Entire Functions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2511.08760

openalex publication_date 2025/11/11 · openalex created_date 2025/11/14 · openalex updated_date 2026/07/28

Abstract

In their papers, Leonetti, Russo, Somaglia, Menet and Papathanasiou posed the question of whether there exists an infinite dimensional vector space of sequences in ℓ_∞ having (except for the zero sequence) an even amount of accumulation points. Here we answer this question in the negative, by showing that this previous set of sequences is not even 3-lineable and, therefore, not lineable.

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