User:Dfeuer/Topological Field

Definition
Let $\struct {!, @, \#}$ be a field with zero $*$.

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

Let ${\&} \colon {!} \setminus \set * \to {!}$ with
 * $\map \& \sim = {\sim}^{-1}$ for each ${\sim} \in {!}$

Then $\struct {!, @, \#, \%}$ is a topological field
 * $\struct {!, @, \#, \%}$ is a Topological Ring.
 * $\&$ is a Continuous Mapping.