Let X denote the subset $(-1,1) \times 0$ of $\mathbb R^2$ and let U be the open ball B(0,1) in $\mathbb R^2$ which contains X. Show that there is no $\epsilon > 0$ s.t the $\epsilon$-neighborhood of X in $R^n$ is contained in U.
I'm not sure what the $\epsilon$ neighborhood of X would be in $\mathbb R^n$. I understand that the points of X in $R^n$ will not be in U, but then X does not have any points in $R^n$ since it is a subset of $R^2$ I'm not sure what i'm missing