From lusk Fri Jun 17 16:25:34 1994
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Subject: Re: Examples
From: Piotr Rudnicki <piotr@cs.ualberta.ca>
To: qed@mcs.anl.gov
Date: 	Fri, 17 Jun 1994 15:24:49 -0600
In-Reply-To: <199406172004.QAA14907@nausicaa.mitre.org> from "F. Javier Thayer" at Jun 17, 94 02:04:22 pm
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Hi:

>    Certainly Trybulec's example requires a real tour-de-force in
> metric space topology. Nevertheless, this example is certainly not one
> to raise any interest among mathematicians. 

I have spent some time with Andrzej discussing the example, it was
not aimed to impress mathematicians.  We hope the example can be used
to discuss how things are done in different QED-like systems.
And also, it is not trivial mathematics.

>                                             Why? Because one of the
> main reasons paracompactness is a useful concept is that it allows us
> to show partitions of unity exist. And the proof of this for the
> really interesting cases (namely differentaible manifolds) is a lot
> easier.

For the sake of continuing the discussion: could Javier explain in a way
similar to Andrzej's, what little theories are involved in the proof
of unity partitioning for differentiable manifolds.


-- 
Piotr (Peter) Rudnicki