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Question on coverings and and their classifying spaces

This is exactly my problem. Aren't $S^2$, $S^2\times\{1,2\}$, $S^2\times\{1,2,3\}$ all covers of $S^2$?

Mar 14, 2011 at 14:22

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Question on coverings and and their classifying spaces

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Mar 14, 2011 at 13:42

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Question on coverings and and their classifying spaces

But with this reasoning $S^2$ would have non-connected covers such as $S^2\times \mathbb{Z}$, too. How does this fit with $[S^2,S^1]=0$ but $[S^1,S^1]=\mathbb{Z}$?

Mar 14, 2011 at 9:00

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Student

Mar 14, 2011 at 3:20

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Question on coverings and and their classifying spaces

Mar 13, 2011 at 22:13

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Editor

Mar 13, 2011 at 21:50