* Re: A well kept secret (A Correction)
@ 2010-01-04 9:13 Reinhard Boerger
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From: Reinhard Boerger @ 2010-01-04 9:13 UTC (permalink / raw)
To: categories
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
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2010-01-04 9:13 A well kept secret (A Correction) Reinhard Boerger
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