Re: Homeomorphic but not isomorphic.

From: lrudolph@xxxxxxxxx (Lee Rudolph)
Date: 1 Apr 2006 19:47:30 -0500

"G. A. Edgar" <edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:

In article <1143802490.909641.253590@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Julien Santini <julien_santini@xxxxxxxxx> wrote:

So why aren't any two separable infinite-dimensional Banach spaces
necessarily isomorphic ?

Because we can write examples... l_1 and l_2 are not isomorphic
as Banach spaces. For example, l_2 is reflexive but l_1 is not.

Now it is true they are isomorphic as linear spaces (requires
Axiom of Choice)

Does it? The obvious way to prove it does. But is it obvious
that there is no inobvious proof, special to the particular
case of l_1 and l_2, that they are isomorphic as linear spaces?
Is it even obvious that there is no (algebraic, discontinuous)
linear automorphism of l_infinity that carries l_1 onto l_2?

Lee Rudolph
.

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Re: Homeomorphic but not isomorphic.
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Re: Homeomorphic but not isomorphic.
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