Identity component
= Identity component
{title2=$G^\circ$}
{wiki}
= Identity component of a topological group
{synonym}
The identity component is the <connected component> containing the <identity element>. It is a closed <normal subgroup>: products and inverses of connected sets through the identity remain in that component, and conjugation preserves it. It need not be open; in the additive group $\mathbb Q$ with its usual topology it is the nonopen singleton $\{0\}$.