From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4637 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Group and abelian group objects in the category of Kelley spaces Date: Sun, 28 Sep 2008 10:19:18 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241020072 14150 80.91.229.2 (29 Apr 2009 15:47:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:52 +0000 (UTC) To: Bill Rowan , categories@mta.ca Original-X-From: rrosebru@mta.ca Sun Sep 28 18:51:54 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 28 Sep 2008 18:51:54 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Kk448-0000YK-VG for categories-list@mta.ca; Sun, 28 Sep 2008 18:44:32 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 133 Original-Lines: 31 Xref: news.gmane.org gmane.science.mathematics.categories:4637 Archived-At: I have not thought deeply on this, but it strikes me that the basic problem is that such a group might not have a uniform topology. Such a group will have, I think, a separately continuous multiplication and hence, if U is a neighborhood of the identity {xU|x \in G} will be a cover, but there would seem no obvious reason for it to have a *-refinement. A continuous homomorphism would be uniformly continuous for those covers, if they do form a uniformity, it seems to me. If only John Isbell were still around to answer this kind of question, a wish I have wished many times since and well before his demise. But have you looked in his uniform spaces book? That is the sort of thing he might well have considered. If I were around the math library, I would look. Michael On Thu, 25 Sep 2008, Bill Rowan wrote: > Hi all, > > Does anyone know of a good place where someone has written down the basic > properties of such objects? As an example, if we have an (abelian, say) > topological group, there is a natural uniform topology on the group such > that the operations are uniformly continuous. Does the same hold for > abelian group objects in the category of Kelley spaces? But anything > would be helpful. > > Bill Rowan > >