If $L$ is a straight line then what is the topology that $L$ inherits as a subspace from $\mathbb{R}_l \times \mathbb{R}$ and as a subspace of $\mathbb{R}_l \times \mathbb{R}_l$ .
I know that the basis of $\mathbb{R}_l \times \mathbb{R}$ is $(a, b] \times (a, b) $ and so the basis of $(\mathbb{R}_l \times \mathbb{R} ) \cap L$ is $((a, b] \times (a, b) ) \cap L$.
I know that the basis of $\mathbb{R}_l \times \mathbb{R}_l$ is $(a, b] \times (a, b] $ and so the basis of $(\mathbb{R}_l \times \mathbb{R} ) \cap L$ is $((a, b] \times (a, b]) \cap L$.
Am I on the right track? I need some hints from here. (not the full answer)
