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Math Help - Line and circle homeomorphic to sphere?

  1. #1
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    Line and circle homeomorphic to sphere?

    Prove that for every n>2, neither the line nor the circle is homeomorphic to S^n, the n-sphere.

    Hint: Use cutpoints.
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  2. #2
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    The hint pretty much says it all. Removing a single point from a line divides it into 1 separated parts. Removing two points from a circle divides it into two separated parts. Neither of those is true for an n-sphere. Remove any finite number of points from an n-sphere and you still have a connected set.
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