Topological ring

Summary

A topological ring is a ring with a topology in which addition, negation and multiplication are continuous. It lets one speak of limits, convergent series and completions inside a ring. The real and complex numbers, the $p$-adic numbers and rings of formal power series with the $(x)$-adic topology are standard examples. A topological field is a topological ring that is a field and in which inversion is also continuous on nonzero elements.