From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5468 Path: news.gmane.org!not-for-mail From: "Reinhard Boerger" Newsgroups: gmane.science.mathematics.categories Subject: Re: A well kept secret (A Correction) Date: Mon, 4 Jan 2010 10:13:23 +0100 Message-ID: Reply-To: "Reinhard Boerger" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1262659581 10407 80.91.229.12 (5 Jan 2010 02:46:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 5 Jan 2010 02:46:21 +0000 (UTC) To: Original-X-From: categories@mta.ca Tue Jan 05 03:46:14 2010 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 1NRzQy-0001ov-J8 for gsmc-categories@m.gmane.org; Tue, 05 Jan 2010 03:46:12 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NRyzp-0007Xf-3y for categories-list@mta.ca; Mon, 04 Jan 2010 22:18:09 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5468 Archived-At: Hello, I wrote: > Some years ago, a functional > analyst needed half an our to prove that homeomorphic Banach spaces have > homemorphic duals, a simple consequence of the fact that all functors > preserve isomorphisms. Sorry, I always meant linear homeomorphisms; I missed to say it explicitly. Without linearity, without linearity the statement is false; e.g. the map l_1 -> l_3, (x_n)_n|_> ((x_n)^3)_n is a homeomorphism, but the dual of l_3 is separable, while the dual of l_1 is not. Greetings Reinhard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]