3 problems

Let $n\geq 2$. Denote by $\hat{\mathcal{C}}_0(\mathbb{R}^n)$ the set of functions vanishing at infinity that have a unique maximum. A subset of a vector space is $k$-lineable if it…

Non-2-lineability conjecture. The set

Let $\mathcal{DP}$ denote the set of Pompeiu derivatives, and let an algebra of functions be called algebrable if it contains an infinitely generated subalgebra. Non-algebrability…