A topological field is a field equipped with a topology for which addition, multiplication, additive inversion, and multiplicative inversion on the nonzero elements are continuous. Thus it is a topological ring whose group of nonzero elements is a topological group.
The real and complex numbers with their usual topologies are topological fields. The rational
numbers inherit a topological-field structure as a subfield of the real
numbers, while the 
-adic numbers provide a non-Archimedean example.
