Totally disconnected group

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

A topological group is termed totally disconnected if it satisfies the following equivalent conditions:

1. Its underlying topological space is a totally disconnected space, i.e., the only non-empty connected subsets are singleton subsets.
2. The connected component of identity is the trivial subgroup.

Relation with other properties

Stronger properties

• Discrete topological group
• Profinite group

Weaker properties

• T0 topological group