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Math Help - Topology (specifically homotopy) question!

  1. #1
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    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.
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  2. #2
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    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
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