Subject: Question about homeomorphisms II
From: Matthias Schmidt <Matthias.Schmidt@itp.uni-leipzig.de>
Date: Thu, 12 May 2005 14:06:59 +0200

This refers to the post 'question about homeomorphisms' of Johannes 
Huebschmann of 4 May 2005.

It was me who asked Johannes Huebschmann to post the question to the forum. 
Unfortunately I have misformulated it. What I actually meant was the 
following:

Assumption: Let f be a surjective continuous map from a closed n-disk onto a 
space X whose restriction to the interior of the disk is a homeomorphism onto 
its image and which has the property that the pre-image of any point of X is
a contractible space. 

Assertion: $X$ is homeomorphic to $D^n$.

As the 2nd example of Kari Ragnarsson's answer (coarsening of topology on the
boundary) shows, the assertion is not true in general. To exclude such cases,
add the assumption that $f$ is open. Does the assertion follow then?

Note: I know the map f quite well, hence I can check any property that might 
be necessary to imply the assumption.

Matthias Schmidt
Institute for Theoretical Physics
University of Leipzig
Germany