Re: Dual of locally compact abelian group
- From: Timothy Murphy <tim@xxxxxxxxxxxxxxxxxxxxxx>
- Date: Sat, 30 Aug 2008 00:42:27 +0200
The World Wide Wade wrote:
Could someone point me to a simple proof (preferably online)
that the dual (with the compact-open topology)
is itself locally compact?
Have you tried looking for this yourself? If you google
"dual group" (including the parentheses) you see an
entry with title
"LOCAL COMPACTNESS OF THE DUAL GROUP USING ASCOLI..."
on the first page of hits.
I had indeed googled, and found this short proof
(modulo Ascoli's theorem).
But I did not find it entirely satisfactory -
So why didn't you mention this in your OP?
Sigh.
I said I was looking for a _simple_ proof.
I did not regard the Ascoli-based proof as simple.
Have you read it, as a matter of interest?
Did you understand it?
--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
.
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