# Initial topology

In my course topology there's a propisition which says the following: suppose $f$ and $g$ are continuous functions and $f \circ g$ is initial then $g$ is initial (I mean with initial that $f \circ g$ and $g$ have the initial topology on their domains).
Now, they ask for a counterexample. I have to give an example where $g$ and $f \circ g$ are initial but $g$ is not a continuous function.