Axiom:Quasinorm Axioms

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

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

Let $\norm{\,\cdot\,}: V \to \R_{\ge 0}$ be a mapping from $V$ to the nonnegative reals $\R_{\ge 0}$.

$\norm{\,\cdot\,}$ satisfies the quasinorm axioms on $V$ $\norm{\,\cdot\,}$ satisifes the axioms:

Also see

 * Definition:Quasinorm