# nLab topological ring

### Context

#### Topology

topology

algebraic topology

## Examples

#### Higher algebra

higher algebra

universal algebra

# Contents

## Definition

A topological ring is a ring internal to Top, a ring object in Top:

a topological space $R$ equipped with the structure of a ring on its underlying set, such that addition and multiplication are continuous functions.

Similarly a topological field is a topological ring whose underlying ring is in fact a field and a topological algebra is a topological ring under a base topological ring (a topological associative algebra).

Shouldn’t we demand that reciprocation be continuous in a topological field? Or does this somehow follow automatically? -Sridhar Ramesh

## Examples

Revised on September 23, 2014 06:07:54 by Urs Schreiber (185.26.182.25)