Let $G$ be a topological group, $A$ be set and $\mu\colon G\times A\to A$ a transitive action.
I'm trying to prove the statement below is false.
There exists only one topology in $A$ such that $\mu$ is a continuous function.
I believe the statement is false because there is more than one such topology. Alas I'm unable to find a counterexample.
How can I find the appropiate topologies to show the statement is false?