From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6433 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Does this topology have a name? Date: Sat, 1 Jan 2011 09:59:48 -0500 (EST) Message-ID: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1293900404 6140 80.91.229.12 (1 Jan 2011 16:46:44 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 1 Jan 2011 16:46:44 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Sat Jan 01 17:46:40 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PZ4bH-0006Gs-RP for gsmc-categories@m.gmane.org; Sat, 01 Jan 2011 17:46:40 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:53466) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PZ4ak-00064w-Rh; Sat, 01 Jan 2011 12:46:06 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PZ4ag-00027i-Mu for categories-list@mlist.mta.ca; Sat, 01 Jan 2011 12:46:02 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6433 Archived-At: Let A be a model of a finitary equational theory and let X be the set of congruences on A. For a,b in A, let M(a,b) = {E} such that E is a congruence on A and aEb. Does this topology have a name? It turns out that this topology is coherent which means, among other things, that if we make the M(a,b) clopen, the result is a Stone space. Obviously in a ring, we could instead use the set of ideals, but aside from the fact that that will include non-prime ideals, the topology is the opposite of the Zariski topology. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]