Definition:Topological Field

Definition
Let $\left({F, +, \circ}\right)$ be a field with zero $0_F$.

Let $\tau$ be a topology on $F$.

Let $\left({F, +, \circ, \tau}\right)$ be a topological division ring.

Then $\left({F,+,\circ,\tau}\right)$ is a topological field.

That is, a topological field is a commutative topological division ring.