"The World Wide Wade" <aderamey.addw@[EMAIL PROTECTED]
> wrote in message
news:aderamey.addw-9BF012.11272013052008@[EMAIL PROTECTED]
> 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
>
Well, that link seems to more than comprehensively answer my question ...
thanks.
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