The metric space $(X,\,d)$ , is called an ultrametric space, if its metric $d$ is an ultrametric, i.e. if $$d(x,\,z) \leqq \max \{d(x,\,y),\,d(y,\,z)\} \quad \forall x,\,y,\,z\in X.$$

Example. The field $\mathbb{Q}$ together with any of its $p$ adic metrics $$d_p(x,\,y) = |x-y|_p,$$ where $|\cdot|_p$ , is the $p$ adic valuation of $\mathbb{Q}$ forms an ultrametric space.