From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4640 Path: news.gmane.org!not-for-mail From: Jeff Egger Newsgroups: gmane.science.mathematics.categories Subject: Re: Group and abelian group objects in the category of Kelley spaces Date: Mon, 29 Sep 2008 03:36:27 -0700 (PDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241020075 14163 80.91.229.2 (29 Apr 2009 15:47:55 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:55 +0000 (UTC) To: categories@mta.ca, Bill Rowan Original-X-From: rrosebru@mta.ca Mon Sep 29 09:49:54 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 29 Sep 2008 09:49:54 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KkI6P-0007Ka-M4 for categories-list@mta.ca; Mon, 29 Sep 2008 09:43:50 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 136 Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:4640 Archived-At: > 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? As others have already noted, the answer is no. One possible solution (assuming you regard this as a defect) is to apply the idea implicit in the definition of Kelley space, not to the category of all topological spaces, but to that of all Tychonov (=uniformisable) spaces. What results is a cartesian closed category (that of "k_R-Tychonov spaces") with somewhat different properties; a group in this category is tautologously uniformisable and, if I recall correctly, is also true that the operations are uniformly continuous. Gabor Lukacs has studied these things and spoken about them at several conferences. Cheers, Jeff. __________________________________________________________________ Yahoo! Canada Toolbar: Search from anywhere on the web, and bookmark your favourite sites. Download it now at http://ca.toolbar.yahoo.com.