Unconditionally closed subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed an unconditionally closed subgroup if $$H$$ is a closed subgroup of $$G$$ for any topology on $$G$$ that turns $$G$$ into a T0 topological group.

Corresponding subset property

 * Unconditionally closed subset is the "subset" version of the property.