Let $X$ be a D11: Set.
Let $\mathcal{T}$ be a D86: Topology on $X$.
The subspace topology of $E \subseteq X$ with respect to $\mathcal{T}$ is the D11: Set \begin{equation} \mathcal{T}_E : = \{ U \cap E \mid U \in \mathcal{T} \} \end{equation}