Totally disconnected group

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.

Stronger properties

 * Weaker than::Discrete topological group
 * Weaker than::Profinite group

Weaker properties

 * Stronger than::T0 topological group