Definition:Topological Field

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

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

Let the mapping $\phi \colon F \setminus \left\{{0_F}\right\} \to F$ be defined as:
 * $\phi \left({x}\right) = x^{-1}$ for each $x \in F \setminus \left\{{0_F}\right\}$

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


 * $(1): \quad \left({F, +, \circ, \tau}\right)$ is a topological ring


 * $(2): \quad \phi$ is a $\tau$-continuous mapping.