Open subset of open subspace is open

Statement

Suppose $X$ is a topological space and $V$ is an open subset of $X$. Suppose $U$ is a subset of $V$ that is an open subset of $V$ under the subspace topology on $V$. Then, $U$ is also an open subset of $X$.

Related facts

• Closed subset of closed subspace is closed
• Dense subset of dense subspace is dense