From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3107 Path: news.gmane.org!not-for-mail From: Gaucher Philippe Newsgroups: gmane.science.mathematics.categories Subject: Re: Alexander Grothendieck on `speculation' Date: Wed, 15 Mar 2006 10:31:40 +0100 Message-ID: <200603151031.40471.gaucher@pps.jussieu.fr> References: <003801c6404f$70d2e020$9ea24e51@brown1> <440C7F19.7080705@math.upenn.edu> <00cf01c647b8$cc302660$e462893e@brown1> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019098 7277 80.91.229.2 (29 Apr 2009 15:31:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:31:38 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Mar 15 19:18:49 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 15 Mar 2006 19:18:49 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FJfA1-000393-Eo for categories-list@mta.ca; Wed, 15 Mar 2006 19:12:09 -0400 User-Agent: KMail/1.8.2 In-Reply-To: <00cf01c647b8$cc302660$e462893e@brown1> Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 53 Original-Lines: 40 Xref: news.gmane.org gmane.science.mathematics.categories:3107 Archived-At: Le Mardi 14 Mars 2006 23:43, vous avez =E9crit=A0: > Jim Stasheff writes: > > This suggests two possibilities: > > > > for the brave, start your own blog for speculations > > for the timid, same input but into a file only you can access > > until late in life and famous you can show how you had the ideas all > > along > > The situation is more complicated in that what could be classed as > speculation may get published as theorem and proof. For example, in > algebraic topology, sometimes proofs of continuity are omitted as if this > was an exercise for the reader, yet the formulation of why the maps are > continuous (if they are necessarily so) may contain a key aspect of what > should be a complete proof. This difficulty was pointed out to me years a= go > by Eldon Dyer in relation to results on local fibration implies global > fibration (for paracompact spaces) where he and Eilenberg felt Dold's pap= er > on this > contained the first complete proof. I have been unable to complete the > proof in Spanier's book, even the second edition. (I sent a correction to > Spanier as the key function in the first edition was not well defined, > after Spanier had replied `Isn't it continuous?') Eldon speculated (!) > that perhaps 50% of published algebraic topology was seriously wrong! My guess is that most of the algebraic topologists assume that the map=20 they are constructing is automatically continuous since the proof will work= =20 for example for simplicial sets (in which there is no continuity to check).= =20 And this argument is wrong : because the category of general topological=20 spaces is not cartesian closed while the category of simplicial sets is=20 cartesian closed. And most of these proofs of continuity become possible on= ly=20 by working in a more convenient category of topological spaces. pg.