User:Dfeuer/Topological Field

Definition
Let $\left({!,@,\#}\right)$ be a field with zero $*$.

Let $\%$ be a Definition:Topology over $!$.

Let ${\&} \colon {!} \setminus \{*\} \to {!}$ with
 * $\&\left({\sim}\right) = {\sim}^{-1}$ for each ${\sim} \in {!}$

Then $\left({!,@,\#,\%}\right)$ is a topological field iff
 * $\left({!,@,\#,\%}\right)$ is a Topological Ring.
 * $\&$ is a Continuous Mapping.