Definition:Non-Archimedean/Norm (Vector Space)/Definition 1
Jump to navigation
Jump to search
Definition
Let $X$ be a vector space.
A norm $\norm {\,\cdot\,} $ on $X$ is non-Archimedean if and only if $\norm {\, \cdot \,}$ satisfies the axiom:
\((\text N 4)\) | $:$ | Ultrametric Inequality: | \(\ds \forall x, y \in X:\) | \(\ds \norm {x + y} \) | \(\ds \le \) | \(\ds \max \set {\norm x, \norm y} \) |