> [!definition] > > $ > \topo_A = \bracs{U \cap A: U \in \topo} > $ > Let $(X, \topo)$ be a [[Topological Space|topological space]], and let $A \subseteq X$. The **relative topology** on $A$ induced by $X$, $\topo_A$, is the intersection of elements of $\topo$ and $A$. > > A set in $\topo_A$ is *relatively* open.