From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6117 Path: news.gmane.org!not-for-mail From: Steven Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: Another question on Grothendieck Date: Sun, 05 Sep 2010 20:51:03 +0100 Message-ID: References: Reply-To: Steven Vickers NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1283777859 12355 80.91.229.12 (6 Sep 2010 12:57:39 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 6 Sep 2010 12:57:39 +0000 (UTC) Cc: To: "Eduardo J. Dubuc" Original-X-From: majordomo@mlist.mta.ca Mon Sep 06 14:57:37 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 1OsbGT-0002dN-5E for gsmc-categories@m.gmane.org; Mon, 06 Sep 2010 14:57:37 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50801) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OsbEs-00042Z-Ri; Mon, 06 Sep 2010 09:55:59 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OsbEp-0001UV-Q0 for categories-list@mlist.mta.ca; Mon, 06 Sep 2010 09:55:56 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6117 Archived-At: 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. On Fri, 03 Sep 2010 22:03:19 -0300, "Eduardo J. Dubuc" wrote: > I confess that I am a little bit confused about what Vaughan is saying. >=20 > This promps me to repeat my posting in other words: >=20 > If a mathematical statement is understood by a reader (the hypotesis, > the conclusion and the proof) >=20 > then the mathematical meaning of any particular notation used should > come up by itself to this reader (that is, it should be clear for him > that only one possible meaning for this particular notation would make > the things work). >=20 > Eduardo [For admin and other information see: http://www.mta.ca/~cat-dist/ ]