Let $X=\mathbb{R}^n$ ($n\ge 1$) be equipped with the natural topology (the one coming from the norms) and let $\lambda$ denote the Lebesgue-measure on $X$.
Let $M\subset X$ be a null set: $\lambda(M)=0$. Is it possible that the closure of $M$ has positive measure, i.e. $\lambda(\overline{M}) > 0$?
Thank you!