Definition:Quasinormed Vector Space

Definition

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

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

Let $\norm \cdot$ be a quasinorm on $V$.

Then we say that $\struct {V, \norm \cdot}$ is a quasinormed vector space.

Also see

• Definition:Quasi-Banach Space