Definition:F-Space

Definition
Let $K$ be a topological field.

Let $\struct {X, \tau}$ be a topological vector space over $K$.

We say that $\struct {X, \tau}$ is an $F$-space there exits a metric $d$ on $X$ such that:


 * $(1): \quad$ $\tau$ is induced by $d$
 * $(2): \quad$ $d$ is an invariant metric
 * $(3): \quad$ $\struct {X, d}$ is a complete metric space.

With $d$ as above, we may also say $\struct {X, d}$ is an $F$-space.