From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5965 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: non-Hausdoff topology Date: Wed, 07 Jul 2010 06:35:07 -0700 Message-ID: References: Reply-To: Vaughan Pratt 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 1278553553 12917 80.91.229.12 (8 Jul 2010 01:45:53 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 8 Jul 2010 01:45:53 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Thu Jul 08 03:45:51 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 1OWgBS-0007Xt-Th for gsmc-categories@m.gmane.org; Thu, 08 Jul 2010 03:45:51 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OWfee-0001jn-PD for categories-list@mta.ca; Wed, 07 Jul 2010 22:11:56 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5965 Archived-At: I thought the point of the Lawson topology was to show the opposite: that the benefits of the Scott topology could be had without having to broaden topology beyond Hausdorff. But if one were to so broaden it, wouldn't it be more natural to do so a la Nachbin and Priestly, with topologized posets? But if you really like the traditional notion of a topological space in all its generality, why insist on the closure conditions on open sets when we know that dropping them gives a category with reasonable properties, namely extensional Chu(Set,2), further improved to a very nice category by dropping extensionality, and generalizable to Chu(Set,K) and yet further to Chu(V,k)? Vaughan Pratt On 7/7/2010 1:31 AM, Paul Taylor wrote: > Non-Hausdorff topologies, in particular the Scott topology, have been > one of the most important features of mathematics applied to computer > science over the past forty years. > > Surely it is now time for this material to be included in the standard > undergraduate curriculum for general topology in pure mathematics > degree programmes. > > I wonder whether "categories" reader have some comments on their > experience of trying to do this? I am thinking of the possible > reactions from both students and colleagues. > > Paul Taylor > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]