Definition:Non-Archimedean/Norm (Vector Space)/Definition 1

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

Also see

 * Equivalence of Definitions of Non-Archimedean Vector Space Norm