Let $(X,\tau)$ be a [normal topological space](/page/Normal%20Topological%20Space), and let $Y \subset X$ be closed in $(X,\tau)$. Equip $Y$ with the [subspace topology](/page/Subspace%20Topology)
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\begin{align*}
\tau_Y := \{Y \cap U : U \in \tau\}.
\end{align*}
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Then $(Y,\tau_Y)$ is a normal [topological space](/page/Topological%20Space).