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).

Examples

Revised on April 6, 2014 22:51:26 by Tim Porter (2.26.40.190)