From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2138 Path: news.gmane.org!not-for-mail From: Alex Simpson Newsgroups: gmane.science.mathematics.categories Subject: Re: Cauchy completeness of Cauchy reals Date: Tue, 28 Jan 2003 01:50:18 +0000 (GMT) Message-ID: <1043718618.3e35e1da24c25@mail.inf.ed.ac.uk> References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1241018437 2668 80.91.229.2 (29 Apr 2009 15:20:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:20:37 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jan 28 19:56:07 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Jan 2003 19:56:07 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18dfTu-00037Z-00 for categories-list@mta.ca; Tue, 28 Jan 2003 19:49:30 -0400 X-Authentication-Warning: topper.inf.ed.ac.uk: apache set sender to als@localhost using -f In-Reply-To: User-Agent: IMP/PHP IMAP webmail program 2.2.8 X-Originating-IP: 130.54.16.90 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 63 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:2138 Archived-At: Andrej Bauer writes: > The map e : 2^N --> [0,1] defined by > > e x = x_0/2 + x_1/4 + x_2/8 + ... > > is epi in the effective topos, but it is not regular epi. This is clearly wrong. Every epi is regular, in a topos. My original statement was correct. In the effective topos, the map from binary representations to Cauchy (= Dedekind) reals is not epi. Alex Simpson Alex Simpson, LFCS, Division of Informatics, Univ. of Edinburgh Email: Alex.Simpson@ed.ac.uk Tel: +44 (0)131 650 5113 Web: http://www.dcs.ed.ac.uk/home/als Fax: +44 (0)131 667 7209