- Thread starter
- #1

- Jan 29, 2012

- 661

I have given a link to the topic there so the OP can see my response.Because there is a homeomorphism between a cylinder and a plane?

- Thread starter Fernando Revilla
- Start date

- Thread starter
- #1

- Jan 29, 2012

- 661

I have given a link to the topic there so the OP can see my response.Because there is a homeomorphism between a cylinder and a plane?

- Thread starter
- #2

- Jan 29, 2012

- 661

$$f:\mathbb{R}^2\setminus\{(0,0)\}\to C\;,\quad f(r\cos\theta,r\sin\theta)=(\cos \theta,\sin\theta,\ln r)\;(r>0)$$

But $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2\setminus\{(0,0)\}$, because