Closed normal subgroup
This article defines a property that can be evaluated for a subgroup of a semitopological group
For a Lie group
When the term closed normal subgroup is used in the context of a Lie group, we mean it with respect to the topology induced by the Lie structure.
For an algebraic group
When a group has both an algebraic group and a Lie group structure, the notion of closed normal subgroup with respect to the algebraic group structure may be strictly stronger than that with respect to the Lie group structure: