Let $E$ be a topological vector space. Then, consider the second dual space $E^{**}$ with a strong topology and let the canonical map $π:E→E^{**}$ be injective. Then prove that the inverse of $π$ is a continuous map from $π(E)$ to $E$.
This problem is given with the following hint.
“Show that the topology induced by the inverse of $π$ is stronger than the original topology of $E$.”
I understand it is sufficient to show that the hint but I don’t know how to show the hint. Please give me an answer.