> [!definition] > > Let $(X, \topo)$ be a [[Topological Space|topological space]]. A set $Y \subset X$ is **locally closed** if for every $x \in Y$, there exists an [[Open Set|open]] [[Neighbourhood|neighbourhood]] $U$ such that $Y \cap U$ is [[Closed Set|closed]] in the [[Relative Topology|relative topology]] on $U$.