Let $W$ be a open set of $\mathbb{R}^n$ and $U$ be path component of $W$.
Consider $p\in U$ and $r\in\mathbb{R}_{>0}$. Prove that if $B_r(p)\subset W$ then $B_r(p)\subset U$ where $B_{r}(p)$ is the open ball with center $p$ of radius $r$.
I am not sure how to proceed . Any hint will be appreciated.