Is the following π-system equal to the topology on the interval I

Question

Consider $I$ an open interval of $\mathbb{R}$.

Now consider this set: $ P=\left \{ I \right \}\cup \left \{(a,b),a\leq b, a,b \in I\right \}$.

This set is obviously a π-system and generates Borel's set. Is this equal to the topology on I ?

If not which set would belong to one and not the other ?

I know a topology is a π-system. How would you describe it if this isn't the one in question.