For (i), try to show that e is homotopic to the zero map. It should be rather clear, geometrically, how to do this.
For (ii), note that
Could anybody help me with this topology question?
i) Prove that every map e: X-> R^n is homotopic to a constant map.
ii) If f: X->S^n is a map that is not onto (surjective), show that f is homtopic to a constant map.
It's part of a past exam paper but it does not come with solutions. Any help on the solution would be greatly appreciated.