Homeomorphic closed subspaces.

Let $X$ be an arbitrary topological space, and $U,V\subseteq X$ two subspaces of $X$ such that $U\cong V$ ($U$ and $V$ are homeomorphic) with respect the subspace topology of $X$. I know examples where $U$ is closed in $X$ and $V$ is not. Is there some conditions to guarantee the next statement:

If $U$ is closed in $X$, then $V$ es closed in $X$.

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