Identity component of a Lie group
= Identity component of a Lie group
{title2=$G^\circ$}
The <connected component> of the identity in a <Lie group> is an open <normal subgroup>. Connected coordinate neighbourhoods prove openness, and conjugation preserves the component of the identity. Every open identity neighbourhood generates it: the generated <subgroup> is open, its other <cosets> are open, and connectedness forces it to be the whole component.