Let $(X, \tau_X)$ and $(Y, \tau_Y)$ be topological spaces, and let $A \subset X$ and $B \subset Y$ be subsets. Then the product topology on $A \times B$ (formed from the subspace topologies $\tau_A$ and $\tau_B$) coincides with the subspace topology on $A \times B$ inherited from $X \times Y$: