I was asked to proove that R^m\R^k (m>k) has the same type of homotopy that S^(m-k-1) .(adsbygoogle = window.adsbygoogle || []).push({});

I know I can use two criterias : the definition and the rectract criterium. The latter is more appealing because of it's "simplicity" but the function

r:[0,1]*X --> X given by (1-t)x + tx/norm(x) yields no results and is in fact a pretty bad choice ...

I have tried in vain to use the definition but I can't find the two functions that will satisfy the conditions.

Please help , I have beem thinking for too long now.

Thanks in advance.

Gagle

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# Homotopy Problem

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