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Thread: parametrization of the k sphere

  1. March 11th 2011, 04:18 AM #1
    Veve
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    parametrization of the k sphere

    How can I show that one cannot parametrize the k sphere S^k by a single parametrization?
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  2. March 11th 2011, 10:50 AM #2
    Bruno J.
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    You should be more specific. What do you mean by a parametrization? What do you mean by a "single parametrization"?

    For example, S^1 can be parametrized as \{(\cos t, \sin t) : t \in \mathbb{R}\}. Why is that no good?
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