From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6497 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: Stone duality for generalized Boolean algebras Date: Tue, 25 Jan 2011 22:51:57 -0200 Message-ID: References: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1296150365 18401 80.91.229.12 (27 Jan 2011 17:46:05 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 27 Jan 2011 17:46:05 +0000 (UTC) Cc: "Fred E.J. Linton" , categories@mta.ca To: George Janelidze Original-X-From: majordomo@mlist.mta.ca Thu Jan 27 18:46:01 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 1PiVux-0000Ow-5M for gsmc-categories@m.gmane.org; Thu, 27 Jan 2011 18:45:59 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:60945) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PiVug-0000Lu-07; Thu, 27 Jan 2011 13:45:42 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PiVuc-0003mW-PK for categories-list@mlist.mta.ca; Thu, 27 Jan 2011 13:45:38 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6497 Archived-At: Dear George, I do not think that the answer to Andrej Bauer question is trivial, as a matter of fact it is not trivial at all. Andrej or any other able mathematician does not have to know that GBA is equivalent to BA/2. Furthermore, I feel that Fred Linton bringing into consideration the analogy with C* algebras is pointing to Andrej some relevant mathematical questions. greetings e.d. George Janelidze wrote: > Dear Fred, > > Please forgive me, but let us distinguish between serious questions and > trivialities: > > Andrej Bauer asked: > > "...How exactly does this extend to generalized Boolean algebras?..." > > And the answer is trivial (without quotation marks): The category GBA of > what he called generalized Boolean algebras is dually equivalent to the > category 1\STONE of pointed Stone spaces. This follows from Stone duality > (since GBA is equivalent to BA/2), but also extends it: just as BA is a > non-full subcategory of GBA, STONE can be considered as a non-full > subcategory of 1\STONE via the functor that adds base points. And this way > the dual equivalence between GBA and 1\STONE indeed extends the Stone > duality. > ... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]