I've been given the question:
Let $ f : X \to Y $ be a continuous map, and suppose we are given (not necessarily equal) continuous maps $ g,h : Y \to X $ such that $ gf \simeq id_X $ and $ fh \simeq id_Y $. Show that $f$ is a homotopy equivalence.
What does it mean for a single function $ f: X \to Y $ to be a homotopy equivalence?
Thanks