Re: Homotopic maps

On Tue, Nov 22, 2005 3:30 PM, <pkornman@xxxxxxx>
wrote:

> If n >= 3, let g:S^n --> S^n be the map g(x_1,
> ...,x_n, x_{n+1}) =
> (x_1, ...., x_n, |x_{n+1}|). Notice that im g lies in
> the closed upper
> hemisphere H of S^n which is a disk D^n. Let h: H -->
> S^n be the map
> the takes Bd D^n to the southpole and maps int D^n
> onto S^n - {south
> pole}. Let f(x) = h(g(x)): S^n -->> S^n. Since f
> factors through a disk
> it's inessential. That is, f is an inessential map of
> S^n onto S^n.
>

Maybe, you forgot that in my original question
f is required to be an INJECTIVE continuous map!!!

.

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