From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3909 Path: news.gmane.org!not-for-mail From: "Ronnie Brown" Newsgroups: gmane.science.mathematics.categories Subject: Re: Homomorphisms on Z^n Date: Sat, 15 Sep 2007 10:02:50 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed; charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019598 10820 80.91.229.2 (29 Apr 2009 15:39:58 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:58 +0000 (UTC) To: "\"Categories list\"" Original-X-From: rrosebru@mta.ca Sat Sep 15 15:46:14 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 15 Sep 2007 15:46:14 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IWcXd-0007SB-Tq for categories-list@mta.ca; Sat, 15 Sep 2007 15:38:53 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 33 Original-Lines: 41 Xref: news.gmane.org gmane.science.mathematics.categories:3909 Archived-At: Michael, I think Christopher Zeemann did something on this in or around the 1950s but cannot at the moment access mathscinet to check. In the 1970s several of us extended Pontrjagin duality: 15. (with P.J. HIGGINS and S.A. MORRIS), ``Countable products of lines and circles: their closed subgroups, quotients and duality properties'', {\em Math. Proc. Camb. Phil. Soc.} 78 (1975) 19-32. in particular defining `strong duality'. Ronnie ----- Original Message ----- From: "Michael Barr" To: "Categories list" Sent: Friday, September 14, 2007 1:34 PM Subject: categories: Homomorphisms on Z^n > Many years ago (at least 45) Harrison mentioned to me that for any n > (including infinite cardinals), Hom(Z^n,Z) = n.Z, in other words the > Z-dual of the product is the sum. This is obviously a very special > property of Z, almost the negation of injectivity. Has anyone on this > list ever seen this before and can give me a reference? > > Michael > > > > > > -- > No virus found in this incoming message. > Checked by AVG Free Edition. > Version: 7.5.487 / Virus Database: 269.13.18/1007 - Release Date: > 13/09/2007 21:48 >