# Connected topological group

From Groupprops

This article defines a property that can be evaluated for a topological group (usually, a T0 topological group)

View a complete list of such properties

## Definition

### Symbol-free definition

A topological group is termed **connected** if it satisfies the following equivalent conditions:

- It is connected as a topological space.
- The connected component of the identity element equals the whole group.

### Equivalence of definitions

Definitions (1) and (2) are clearly equivalent.