Ultrametric space

In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to ${\displaystyle d(x,z)\leq \max \left\{d(x,y),d(y,z)\right\}}$ for all ${\displaystyle x}$, ${\displaystyle y}$, and ${\displaystyle z}$. Sometimes the associated metric is also called a non-Archimedean metric or super-metric.