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

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.