Re: Question about a mapping

From: Wassily Dali (jsr142_at_sbcglobal.net)
Date: 06/30/04 

Date: 30 Jun 2004 00:21:04 -0700

> That statement is incorrect, since 0 is not in the image of the upper
> half-plane.

And if "upper half-plane" refers to {z in C union {infinity} | Im (z) > 0},
then the statement is correct?

(Since this maps takes infinity to zero).

israel@math.ubc.ca (Robert Israel) wrote in message news:<cbt9sg$ra2$1@nntp.itservices.ubc.ca>...
> In article <94027e8c.0406291518.10a416b0@posting.google.com>,
> Wassily Dali <jsr142@sbcglobal.net> wrote:
> >I have a question regarding the map z -> e^(2*pi*i*z) where i is
> >sqrt(-1), Im(z) > 0, and the statement: "Note that this map maps the
> >upper half-plane analytically onto the unit disk, and takes infinity
> >to the origin."
> >
> >The last part of the statement is clear to me. Question: why does this
> >map the upper half-plane onto the unit disk?
>
> That statement is incorrect, since 0 is not in the image of the upper
> half-plane.
>
> >And what does it mean
> >exactly to say 'maps analytically?'
>
> Just that it is an analytic function on the upper half-plane.
>
> Robert Israel israel@math.ubc.ca
> Department of Mathematics http://www.math.ubc.ca/~israel
> University of British Columbia
> Vancouver, BC, Canada V6T 1Z2

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