3
$\begingroup$

As the title, I am thinking $$f :\ S^1\times I / S^1\times \lbrace1\rbrace \rightarrow D^2$$ as $f(x,y,z)= (x,y)$ and $$g :\ D^2 \rightarrow S^1\times I / S^1\times\lbrace1\rbrace$$ as $g(x,y)=(x,y,1-\sqrt{x^2+y^2})$.

Just remains to show $f$ and $g$ are continuous.

  • 0
    Try mapping $(x,t)$ to $tx$ in $\mathbb{R}^2$.2012-08-01
  • 0
    Use the center of a circle in the plane as the cone point. The radii from the center gives the cone on $S^1$, so it is a $D^2$2012-08-01
  • 1
    Recall a continuous, bijective map from a compact space to a Hausdorff space is a homeomorphism.2012-08-01

1 Answers 1