From lusk Fri Jun 17 17:01:27 1994 Received: from linus.mitre.org (linus.mitre.org [129.83.10.1]) by antares.mcs.anl.gov (8.6.4/8.6.4) with ESMTP id RAA27086 for ; Fri, 17 Jun 1994 17:01:14 -0500 Received: from nausicaa.mitre.org (nausicaa.mitre.org [129.83.10.45]) by linus.mitre.org (8.6.7/RCF-6S) with ESMTP id SAA13877; Fri, 17 Jun 1994 18:01:11 -0400 Received: from localhost (localhost [127.0.0.1]) by nausicaa.mitre.org (8.6.7/RCF-6C) with ESMTP id SAA14969; Fri, 17 Jun 1994 18:01:09 -0400 Message-Id: <199406172201.SAA14969@nausicaa.mitre.org> To: qed@mcs.anl.gov cc: jt@linus.mitre.org Subject: Re: Examples In-reply-to: Your message of "Fri, 17 Jun 1994 15:24:49 MDT." <94Jun17.152454-0600.18525-2@scapa.cs.ualberta.ca> Date: Fri, 17 Jun 1994 18:01:07 -0400 From: "F. Javier Thayer" I believe I implied that the theorem in Trybulec's example is highly non-trivial. I do claim however that one can do rigorous mathematics that would appeal to a wider community of individuals with less work. I don't believe we should take the alternate approach of doing partititions of unity on differentiable manifolds either. I mentioned this as an explanation of the fact that most mathematicians are terribly interested in this result at all and get can get by without ever having heard of it. As far as the 'little theories' required to prove unity partitioning for differentiable manifolds, I don't know the answer, but it obviously requires a lot more stuff than the metric space approach Trybulec mentioned and is not a good candidate for a test case. Notice, however, it falls almost for free from other developments in a standard differentiable manifolds course (actually the fact that manifolds are locally compact helps), and one also gets better properties for the partitions. Javier