Definition:Quasinorm

Definition
Let $\struct {R, +, \circ}$ be a division ring with norm $\norm {\,\cdot\,}_R$.

Let $V$ be a vector space over $R$.

A quasinorm on $V$ is a map from $V$ to the nonnegative reals:


 * $\norm{\,\cdot\,}: V \to \R_{\ge 0}$

satisfying the quasinorm axioms: