If $X$ is a topological group, and $A, B, C$ are subgroups where $B$ contains $C$, and $C$ is contained in the intersection of $A$ and $B$.
If $C$ is closed in $B$ then will it be closed in the intersection of $A$ and $B$?
If $X$ is a topological group, and $A, B, C$ are subgroups where $B$ contains $C$, and $C$ is contained in the intersection of $A$ and $B$.
If $C$ is closed in $B$ then will it be closed in the intersection of $A$ and $B$?