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