From lusk Fri Jun 17 16:25:34 1994 Received: from scapa.cs.ualberta.ca (scapa.cs.ualberta.ca [129.128.4.44]) by antares.mcs.anl.gov (8.6.4/8.6.4) with SMTP id QAA26085 for ; Fri, 17 Jun 1994 16:25:05 -0500 Received: from sedalia.cs.ualberta.ca by scapa.cs.ualberta.ca id <18525-2>; Fri, 17 Jun 1994 15:24:54 -0600 Subject: Re: Examples From: Piotr Rudnicki 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 X-Mailer: ELM [version 2.4 PL23] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Content-Length: 948 Message-Id: <94Jun17.152454-0600.18525-2@scapa.cs.ualberta.ca> 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