Problem 5. Let $(Y, \mathcal{T})$ be a topological space, and let $A \subset X \subset Y$ be subsets.
We can consider two topologies on $A$: the subspace topology $\mathcal{T}_A$ on $A \subset Y$ considered as a subset
of $Y$, and the subspace topology $(\mathcal{T}_X)_A$ on $A \subset X$ considered a subset of $X$ (where $X$ is regarded
as a topological space via its subspace topology $\mathcal{T}_X$ inherited from $Y)$.
Prove that $\mathcal{T}_A = (\mathcal{T}_X)_A$
