An ultrametric space is a special kind of metric space in which the triangle inequality is replaced with $d(x,z)\leq\max\left\{d(x,y),d(y,z)\right\}$.
Is a p-adic number field and a finite algebraic extension of it ultrametric?
This theorem asserts that a p-adic number field and a finite algebraic extension of it are not ultrametric:
