From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6124 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: Another question on Grothendieck Date: Mon, 06 Sep 2010 14:53:45 -0300 Message-ID: References: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1283862919 933 80.91.229.12 (7 Sep 2010 12:35:19 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 7 Sep 2010 12:35:19 +0000 (UTC) Cc: categories@mta.ca To: Steven Vickers Original-X-From: majordomo@mlist.mta.ca Tue Sep 07 14:35:17 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OsxOK-0006hf-H5 for gsmc-categories@m.gmane.org; Tue, 07 Sep 2010 14:35:12 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:53531) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OsxN9-0006RT-Rs; Tue, 07 Sep 2010 09:33:59 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OsxN6-000066-5A for categories-list@mlist.mta.ca; Tue, 07 Sep 2010 09:33:56 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6124 Archived-At: Dear Steve, I was already aware that my statement "only one possible meaning"? was much too general and I myself speculated (at the time of posting the msage) about many possible exceptions when literally interpreting my statement. But I decided to leave it like that. Luckily it was understood as I meant (private msages). I clarify to you and to those that may rise similar exceptions: The Tohoku paper is just plain old classical mathematics (*), and nothing of the sort of your example is to be found there. I imagine on the other hand that in your papers you do not let the reader stay in the doubt about the meaning of these two possible meanings. (*) where you can of course point out if some reasoning is constructively valid (an exceptional example of this is the chapter on field extensions in the second edition of the classical Van der Waerden book). e.d. Steven Vickers wrote: > Dear Eduardo, > > I have written papers that deliberately have two possible meanings: one > classical point-set and one constructive point-free. > > That is to say, the development in terms of points is done under logical > (geometric) constraints that enable it to be interpreted in topos-valid > point-free topology (locales), but it can be interpreted directly in > point-set topology if one accepts classical logic. > > I did this for expositional reasons, to help classical topologists > understand the topological content of what I was doing. > > See: > > "Localic completion of generalized metric spaces I" > "The connected Vietoris powelocale" > > Is this compatible with what you were saying about "only one possible > meaning"? > > Regards, > > Steve Vickers. > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]