From psh@wins.uva.nl Thu Oct 7 18:12:36 1999
Return-Path:
Received: from mbox.wins.uva.nl (root@mbox.wins.uva.nl [146.50.16.22])
by zorn2.math.leidenuniv.nl (8.9.3/8.8.7) with ESMTP id SAA29186
for ; Thu, 7 Oct 1999 18:12:36 +0200
Received: from noot.wins.uva.nl
by mbox.wins.uva.nl with ESMTP (sendmail 8.8.7/config 8.9).
id SAA19744; Thu, 7 Oct 1999 18:10:54 +0200 (MET DST)
Received: from localhost
by noot.wins.uva.nl (sendmail 8.8.7/config 8.9).
id SAA13244; Thu, 7 Oct 1999 18:10:52 +0200 (MET DST)
Message-Id: <199910071610.SAA13244@noot.wins.uva.nl>
Date: Thu, 7 Oct 1999 18:10:52 +0200 (MET DST)
From: psh@wins.uva.nl (Peter Stevenhagen)
X-Organisation: Faculty of Mathematics, Computer Science, Physics & Astronomy
University of Amsterdam
The Netherlands
X-Address: See http://www.wins.uva.nl/location
To: dinakar@its.caltech.edu
Subject: FANF
Cc: desmit@math.leidenuniv.nl, psh@wins.uva.nl
Status: RO
Dear Professor Ramakrishnan,
You may be pleased to hear that we have selected your
book `Fourier analysis on number fields' as a text
for our local graduate student seminar in number theory.
We are a bit confused by the conventions on topological groups
that you introduce in the first chapter.
Topological groups are not assumed to be T_1 (page 5), so for
all we know the topology might be indiscrete. But how can we
then prove that the closure of an abelian subgroup (such as {e})
is always abelian (exercise 1.7)?
Even more troubling, you prove in theorem 1.18 (page 31) that
subgroups of finite index in a profinite group are always open.
If we take G to be a countably infinite product of fields F2
(of two elements), then G is a topological ring. Any maximal ideal
containing the direct sum of all F2's inside the direct product G
is an additive subgroup of index 2 that is not open in G.
Are we missing something? We would appreciate your comments.
Yours sincerely,
Bart de Smit and Peter Stevenhagen.