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Re: Dual vector spaces
Posted:
Jun 27, 2006 10:04 AM
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In article <e7qfv1$67o$1@glue.ucr.edu>, John Baez
<baez@math.removethis.ucr.andthis.edu> wrote:
> Every finite-dimensional vector space is isomorphic to
> its dual.
>
> Is it true that no infinite-dimensional vector space is
> isomorphic to its dual?
>
> Feel free to pick your favorite field if that helps.
>
> Feel free to use the axiom of choice if that helps, too.
> But please let me know if you're using it.
>
>
> (I emphasize that I'm talking about a purely algebraic
> question, not about topological vector spaces. Every
> Hilbert space is isomorphic to its *topological*
> dual, consisting of *continuous* linear functionals.
> That's not what I'm talking about. I'm talking about
> the *algebraic* dual of a vector space, consisting of
> *all* linear functionals. And by "isomorphism", I just
> mean a linear operator with a linear inverse.)
>
>
Is it true, using AC, that if a vector space has infinite
Hamel dimension m, then the dual has Hamel dimension 2^m ?
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
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