(See attached file for full problem description with proper symbols and equation)
Let be a surjective continuous map between topological spaces. Show that:
a) If f is an identification mp, then for any pace Z and any map the composition is continuous if and only if g is continuous.
b) If, for any space Z and any map , the composition is continuous if and only if g is continuous, then f is an identification map.
This is a proof regarding a surjective continuous map.