Re: Geometry with curve, homeomorphism.


"Jannick Asmus" <jannick.newsREMOVE_ME@xxxxxx> wrote in message
news:gal4k4$mfm$1@xxxxxxxxxxxx
On 15.09.2008 09:43, mina_world wrote:
Hello teacher~

Even if a curve is injective,
it does not have to be a homeomorphism onto its image.

This is the case for the Descartes folium a : (-1, oo) -> R^2
given by a(t) = ( 3t / (1 + t^3) , 3t^2 / (1 + t^3) )

http://board-2.blueweb.co.kr/user/math565/data/math/desfol.jpg

----------------------------------------------------------------
Can you understand it
"it does not have to be a homeomorphism onto its image" ?

Hint: What happens if you remove a carefully chosen point?

http://board-2.blueweb.co.kr/user/math565/data/math/point.jpg

How can you show that this is connected at origin ?


.

Quantcast