Prove that a closed ball is an open set in ultrametric space

Question

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Am I correct?

Let $y \in \overline{B_r}(x)$ then $d(y,x) \leq r$. Take $B_{r}(y)$, then $z \in B_{r}(y)\subseteq \overline{B_r}(x)$, because $d(x,z)=\max\{d(x,y),d(y,z)\}\leq r$.