From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4992 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Topology on cohomology groups Date: Fri, 19 Jun 2009 10:26:13 +0100 Message-ID: Reply-To: Steve Vickers NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1245443049 26518 80.91.229.12 (19 Jun 2009 20:24:09 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 19 Jun 2009 20:24:09 +0000 (UTC) To: Categories Original-X-From: categories@mta.ca Fri Jun 19 22:24:07 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 1MHkd3-0004ab-9P for gsmc-categories@m.gmane.org; Fri, 19 Jun 2009 22:24:05 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MHk1h-000533-CR for categories-list@mta.ca; Fri, 19 Jun 2009 16:45:29 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4992 Archived-At: A cohomology group can easily be an infinite power of the coefficient group. But such a group has a natural non-discrete topology, namely the compact-open (which in this case is also the product topology). Are there approaches to cohomology that, as part of the process, also supply topologies on the cohomology groups? [I'm trying to understand the topos-theoretic account of cohomology as in Johnstone's "Topos Theory". But it looks heavily dependent on having a classical base topos, since it uses the classical proof of sufficiency of injectives (together with the existence of Barr covers) to deduce the same property internally in any Grothendieck topos. For a more fully constructive theory I wonder if one needs to take better care of the topologies.] Steve Vickers. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]