Show that 'Unit circle\{(0,1)} is homeomorphic to R'...

I need the function..Thank you in advance..

Printable View

- Oct 31st 2009, 09:52 PMmath.djHomeomorphism
Show that 'Unit circle\{(0,1)} is homeomorphic to R'...

I need the function..Thank you in advance.. - Nov 1st 2009, 12:20 AMtonio

Stereographic projection: take al the "rays" (in fact, straight lines) through (0,1) with slope , and match the point on the circle they pass through with the one where they intersect the x-axis:

if the line is , then the intersection with the circle is at the point , and the intersection with the x-axis is .

Tonio