0708-1300/Covering Product: Difference between revisions
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Think about an infinite product of copies of <math>S^1</math>. Even more, think about the possibility of this space having a universal covering space. At some point it is probably needed that <math>\mathbb{Z}^n\not\ |
Think about an infinite product of copies of <math>S^1</math>. Even more, think about the possibility of this space having a universal covering space. At some point it is probably needed that <math>\mathbb{Z}^n\not\cong\mathbb{Z}^m</math> for <math>n\neq m</math>. It is interesting to produce a proof of this using the less knowledge you can. A possible idea is [[0708-1300/fact|here]]. |
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Latest revision as of 16:16, 18 February 2008
Think about an infinite product of copies of [math]\displaystyle{ S^1 }[/math]. Even more, think about the possibility of this space having a universal covering space. At some point it is probably needed that [math]\displaystyle{ \mathbb{Z}^n\not\cong\mathbb{Z}^m }[/math] for [math]\displaystyle{ n\neq m }[/math]. It is interesting to produce a proof of this using the less knowledge you can. A possible idea is here.
