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I'm trying to solve this question:

My attempt of solution:

Note first I use the stereographic projection to see the sphere is homeomorphic to the plane with a point at infinity, after this we get this infinite block with height 1 with a segment of height 1 at infinity.

Am I right? I fell I'm wrong, this space seems very weird.

Thanks

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Just draw a 2-sphere in a 2-sphere and define the space in between to be filled.

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  • $\begingroup$ basically it is a 2-dimensional annulus en.wikipedia.org/wiki/Annulus_(mathematics) $\endgroup$ – Daniel Valenzuela Sep 24 '14 at 18:11
  • $\begingroup$ I'm sorry, but Why? $\endgroup$ – user85493 Sep 24 '14 at 18:19
  • $\begingroup$ the "$\times I$" means that you can paramatrize it. So just parametrize it, eg. by saying that the inner sphere is $0$ and the outer sphere is $1$. $\endgroup$ – Daniel Valenzuela Sep 24 '14 at 18:23
  • $\begingroup$ and by this I mean that $X \times I$ is a collection of $(X,t)$ with $t \in I$. $\endgroup$ – Daniel Valenzuela Sep 24 '14 at 18:23
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    $\begingroup$ yes and you are reminding me that I am really hungry. $\endgroup$ – Daniel Valenzuela Sep 24 '14 at 18:27

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