I have difficulties solving the following exercise:
Prove that if f and g are continuous functions from a topological space X to , then f+g and fg are continuous.
The hint says: Apply this theorem: let , and be topological spaces and let and be continuous functions. Then g(f): is continuous.
and use the easy facts that the maps (x,y) to x+y and xy are continuous (where defined).
I really don't know how to use the hint, i can't imagine that this exercise is difficult.
Thanks for help.