From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5369 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Preprint: "Ionads" Date: 15 Dec 2009 04:48:48 +0000 Message-ID: References: Reply-To: Richard Garner NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset=ISO-8859-1 X-Trace: ger.gmane.org 1260921637 30410 80.91.229.12 (16 Dec 2009 00:00:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 16 Dec 2009 00:00:37 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Wed Dec 16 01:00:30 2009 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 4.50) id 1NKhJZ-0005LM-EK for gsmc-categories@m.gmane.org; Wed, 16 Dec 2009 01:00:25 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NKgt3-0004oT-FR for categories-list@mta.ca; Tue, 15 Dec 2009 19:33:01 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5369 Archived-At: Dear all, At CT09, I gave a talk on what I then was calling "generalised topological spaces", and now have named "ionads". A few people asked if I had anything written down concerning the content of that talk; this is to say that I now do. A preprint is available at http://arxiv.org/abs/0912.1415 An abstract follows. Richard --- The notion of Grothendieck topos may be considered as a generalisation of that of topological space, one in which the points of the space may have non-trivial automorphisms. However, the analogy is not precise, since in a topological space, it is the points which have conceptual priority over the open sets, whereas in a topos it is the other way around. Hence a topos is more correctly regarded as a generalised locale, than as a generalised space. In this note, we introduce a new notion---that of ionad---which stands in the same relationship to a topological space as a (Grothendieck) topos does to a locale. Some basic aspects of the theory are developed and applications to topology, logic and geometry are discussed. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]