Definition:Non-Archimedean/Norm (Vector Space)

Definition
A norm $\norm {\,\cdot\,} $ on a vector space $X$ is non-Archimedean $\norm {\, \cdot \,}$ satisfies the axiom:

The pair $\struct {X, \norm {\, \cdot \, } }$ is a non-Archimedean normed vector space.