From: Alex Simpson <als@inf.ed.ac.uk>
To: categories@mta.ca
Subject: Re: Cauchy completeness of Cauchy reals
Date: Tue, 28 Jan 2003 01:50:18 +0000 (GMT) [thread overview]
Message-ID: <1043718618.3e35e1da24c25@mail.inf.ed.ac.uk> (raw)
In-Reply-To: <vkafzrepk18.fsf@laurie.fmf.uni-lj.si>
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
next prev parent reply other threads:[~2003-01-28 1:50 UTC|newest]
Thread overview: 21+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-01-27 17:41 Andrej Bauer
2003-01-28 1:50 ` Alex Simpson [this message]
-- strict thread matches above, loose matches on Subject: below --
2003-01-28 20:51 Dusko Pavlovic
2003-01-29 2:00 ` Toby Bartels
2003-01-29 8:35 ` Alex Simpson
2003-02-04 9:15 ` Dusko Pavlovic
2003-02-05 20:56 ` Toby Bartels
2003-01-28 9:44 Andrej Bauer
2003-01-16 23:05 Generalization of Browder's F.P. Theorem? Michael Barr
2003-01-21 18:11 ` Andrej Bauer
2003-01-22 10:13 ` Cauchy completeness of Cauchy reals Martin Escardo
2003-01-22 23:33 ` Dusko Pavlovic
2003-01-24 8:51 ` Martin Escardo
2003-01-25 2:21 ` Dusko Pavlovic
2003-01-25 16:24 ` Prof. Peter Johnstone
2003-01-27 3:57 ` Alex Simpson
2003-01-23 6:29 ` Vaughan Pratt
2003-02-04 0:47 ` Vaughan Pratt
2003-02-05 16:06 ` Prof. Peter Johnstone
2003-01-23 9:50 ` Mamuka Jibladze
2003-01-24 1:34 ` Ross Street
2003-01-24 16:56 ` Dusko Pavlovic
2003-01-24 19:48 ` Dusko Pavlovic
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