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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 atprecisely one (and only one) point is $n$-lineable but not $(n+2)$-lineable.This result complements some recent published works on an open questionoriginally posed by Vladimir I. Gurariy (1935--2005) in 2003.

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