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arXiv · 2312.05004

On the set of functions that vanish at infinity and have a unique maximum

Anderson Barbosa·Gustavo Araújo
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Abstract

In this paper, we show that the set of continuous functions defined on $\mathbb{R}^n$ that approach zero at infinity and attain their maximum at precisely one (and only one) point is $n$-lineable but not $(n+2)$-lineable. This result complements some recent published works on an open question originally posed by Vladimir I. Gurariy (1935--2005) in 2003.

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Anderson Barbosa, Gustavo Araújo. 2023-12-08. On the set of functions that vanish at infinity and have a unique maximum. https://arxiv.org/abs/2312.05004

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