In article <48295200$0$30466$afc38c87@[EMAIL PROTECTED]
>,
"Peter Webb" <webbfamily@[EMAIL PROTECTED]
> wrote:
> All this talk of Mobius strips makes me wonder ...
>
> There are lots of 2D surfaces that can be embedded into 3 dimensions,
for
> example the infinite plane (R^2), sphere, torus etc can all be embedded
in
> R^3.
>
> There are some 2D surfaces which cannot, and (I believe) require 4
> dimensions such as the Klein bottle and cross-cap.
>
> Is 4D sufficient for all unbounded surfaces? All surfaces? Can a surface
be
> constructed which needs 5 dimensions?
Yes, yes, and no. See the Whitney Embeding Theorem,
http://en.wikipedia.org/wiki/Whitney_embedding_theorem
> And please, I can't provide a definition of a surface, other than it is
a 2D
> structure which can be represented by a reasonably behaved function,
such as
> everywhere continuous (analytic even?).
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