From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6488 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Stone duality for generalized Boolean algebras Date: Fri, 21 Jan 2011 17:39:02 -0500 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1295783889 28306 80.91.229.12 (23 Jan 2011 11:58:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 23 Jan 2011 11:58:09 +0000 (UTC) To: "categories" Original-X-From: majordomo@mlist.mta.ca Sun Jan 23 12:58:03 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 1Pgya2-000332-OD for gsmc-categories@m.gmane.org; Sun, 23 Jan 2011 12:58:02 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:49408) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PgyZj-0007L4-WE; Sun, 23 Jan 2011 07:57:44 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PgyZg-0004EL-Dr for categories-list@mlist.mta.ca; Sun, 23 Jan 2011 07:57:40 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6488 Archived-At: The Boolean rng counterpart to the Stone duality, identifying Boolean algebras with the opposite of compact T2 0-dim'l spaces, exploits the fact that the category of boolean rngs amounts to the category of *augmented* Boolean algebras (the slice category BA | 2 of 2-valued boolean homomorphisms from Boolean algebras) -- true because *kernel* gives an equivalence from latter to former -- hence is equivalent to the opposite of *pointed* compact T2 0-dim'l spaces (and base-point-preserving continuous functions). While the complement of the base point (in such a pointed space) may be locally compact, that observation is far from functorial, = so there's not much good any category of locally compact T2 0-dim'l spaces will do you. HTH. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]