I don't really know why, but I'm having trouble actually building deformation retractions, although I understand the concepts behind homotopies, etc.(adsbygoogle = window.adsbygoogle || []).push({});

For example, when constructing a deformation retraction for [tex]\mathbb{R}^n-\{0\}[/tex] to [tex]S^{n-1}[/tex], I found that you could define the mapping [tex]F(x,t) = (\frac{x_1}{t||x||+(1-t)},...,\frac{x_n}{t||x||+(1-t)})[/tex]. However, I still don't see how you can think of such a thing..

I get the idea of turning the x_ns into unit vectors, but I don't understand the intuition behind the +(1-t), etc.

Anyone want to give some advice?

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# Constructing Explicit Deformation Retractions

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