Closed subgroup of algebraic group

Definition
Suppose $$G$$ is an algebraic group over a field $$K$$ and $$H$$ is a subgroup of $$G$$. We say that $$H$$ is a closed subgroup of $$G$$ if $$H$$ is a closed subgroup of $$G$$ when we equip $$G$$ with the natural topological group structure arising from the Zariski topology.

Facts

 * Closed subgroup of algebraic group inherits algebraic group structure