Topological field

Summary

A topological field is a field with a topology in which addition, multiplication, negation and inversion are continuous, see the definition. It is a field that is also a topological ring and in which taking inverses is continuous. The real numbers, the complex numbers, the p-adic numbers and every field with an absolute value are topological fields. The notion is the common setting for analysis over fields other than $\R$ and $\C$.