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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 $B$?

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    The fact that these are subgroups of a group is completely irrelevant here.2016-02-02

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