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If $f, g: S^1\to \mathbb C$ are two functions, what is a homotopy from $f=\frac{g}{\vert g\vert}$ to $g$?

I just want to check whether my homotopy $H(x,t): (1-t)f+tg$ where $x \in S^1, t \in [0,1]$ is correct.

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Please specify domain and codomain of your functions. –  Stefan Hamcke Jun 11 '13 at 18:37
sorry, $X=S^1, Y=\mathbb{C}$ –  topa Jun 11 '13 at 18:38
If you want to check whether your homotopy is right, I suggest you post it. –  msh210 Jun 11 '13 at 18:38
$(1-t)f+tg$ but this would work for any two functions, that's why I'm unsure –  topa Jun 11 '13 at 18:39
I (and I think @StefanH.) meant you should edit the info into the question. Comments are ephemeral by design. A question in which you include all you know already will get you answers more directly addressing what you don't. –  msh210 Jun 11 '13 at 18:40

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