Definition 4

A topological division ring is a set $K$ carrying a division ring structure and a topology compatible with the ring structure of $K$, and satisfying in addition the following axiom:

(KT) The mapping $x \to x^{-1}$ of $K^*$ into $K^*$ is continuous.

A commutative topological division ring is called a topological field.

A division ring structure and a topology on a set $K$ are said to be compatible if the corresponding ring structure and the topology are compatible and if in addition axiom (KT) is satisfied.