Sobre a lineabilidade do conjunto das funções contínuas que atingem o máximo em um único ponto.

Abstract

In this work we present a proof of the problem posed by Vladimir I. Gurariy, in 2003, which refers to the existence or not of a vector space, except for the null vector, in the set Cˆ(R), of all continuous real functions defined on R that attain its maximum at a single point of its domain. In the initial chapters, we present all the concepts and preliminary results for the full understanding of that proof. In the last chapter, we initially verify the 2-lineability of Cˆ(R) and then we conclude it by proving the non 3-lineability of this set, using Moore’s Theorem.