Re: Contractible metric space

From: Stuart M Newberger (smnewberger_at_comcast.net)
Date: 02/28/05 

Date: 28 Feb 2005 03:42:05 -0800

Lasse wrote:
> The idea of the metric is to ensure that points in the complex plane
> which converge to i will converge to the endpoint (1,*) in the new
> space, while the points (t,*) with t\in (0,1) cannot be accumulated
on
> by points in the original set Y.
>
> So the point is that the endpoints of the line segments in Y, i.e.,
the
> points
> x_n := e^{\pi/2 - \pi/2n}
> converge to (1,*). However, the points
> x_n(t) := t x_n
> do not converge to (t,*). Am I missing something?
>
> Lasse

The distance from d(x_n,(1,*)) converges to Min(1+|i|,|1-i|)=2^1/2>0 so
the sequence does not converge to (1,*) .Regards,Stuart M Newberger