Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: ping José Carlos Santos
Replies: 1   Last Post: Dec 23, 2012 1:40 PM

 Messages: [ Previous | Next ]
 Jose Carlos Santos Posts: 4,896 Registered: 12/4/04
Re: ping José Carlos Santos
Posted: Dec 23, 2012 1:40 PM

On 21/12/2012 08:28, Rupert wrote:

> Previously I made the assertion to you that if f is a mapping from a
> Euclidean space E^n into a Euclidean space E^m which maps straight
> lines into straight lines and whose range has three points in general
> position, then it follows that f is an affine transformation.
>
> As Guowu Yao of Tsinghau University has pointed out to me this is
> false. For consider the case n=m=2 and f acts as the identity on a
> straight line and collapses the rest of the plane to a point not on
> the line.
>
> However I believe that I can fix this. For example, I think that I can
> prove that if f is a mapping from a Euclidean space E^n into E^n,
> which maps straight lines into straight lines, and whose range
> contains n+2 distinct points any n+1 of which are in general position,
> then f is an affine transformation.
>
> I hope to publish this sometime soon. I will keep you posted on the
> details.

Thank you. I'll be waiting for your proof.

Best regards,

Jose Carlos Santos

Date Subject Author
12/21/12 Rupert
12/23/12 Jose Carlos Santos