# Math Help - Topology (specifically homotopy) question!

1. ## Topology (specifically homotopy) question!

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.

Thanks.

2. 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 $S^n \setminus \{x_0\} \cong \mathbb{R}^n$