From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5950 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: The humility topos Date: Fri, 2 Jul 2010 11:41:46 -0400 (EDT) Message-ID: References: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1278261260 21594 80.91.229.12 (4 Jul 2010 16:34:20 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 4 Jul 2010 16:34:20 +0000 (UTC) Cc: Dusko Pavlovic , Categories list To: "Eduardo J. Dubuc" Original-X-From: categories@mta.ca Sun Jul 04 18:34:18 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OVS91-0000td-Rc for gsmc-categories@m.gmane.org; Sun, 04 Jul 2010 18:34:16 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OVRjZ-00073I-Ss for categories-list@mta.ca; Sun, 04 Jul 2010 13:07:57 -0300 In-Reply-To: <4C2DFFD3.8050406@dm.uba.ar> Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5950 Archived-At: The older name for topology was "analysis situs", analysis of place. Why= =20 that was changed is unknown to me, but the topo- root is just Greek for=20 place and it would be a stretch to assume anything else without good=20 evidence. A French mathematician named, IIRC, Jean Pont wrote a book called,=20 "L'Histoire de la topologie alg=E9brique avant Poincar=E9" that traces=20 topology, at least algebraic topologie to Euler's solution to the bridges= =20 of K=F6nigsberg problem. I think V-F+E =3D 2 came next. Michael On Fri, 2 Jul 2010, Eduardo J. Dubuc wrote: > Grothendieck introduced the term "topos" simply out of "topology" and=20 > "topological space". > > we should wonder who and why introduced "topology" and "topological spa= ce". > > Dusko Pavlovic wrote: >> It might be fair to remember that "Topoi" is the title of 6th book or >> Aristotle's Organon. "On Categories" is the title of the 1st book of >> Organon. >> Both concepts were very actively used by scolastic philosophers. Mayb= e we >> are their heirs of some sort ;) >> >> It would be interesting to know about the motivations of people who >> introduced these terms into mathematics. I think that MacLane said at= one >> point that there was a terminological link through Rudolf Carnap, thu= s >> through neokantians. The notion of categories plays a prominent role = in >> Kant's first Critique. But it is even more interesting if the term to= pos >> was introduced with an intentional reference to *dialectics*, which i= s >> what that part of Organon is about. >> >> -- dusko [For admin and other information see: http://www.mta.ca/~cat-dist/ ]