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From: Maximilian Rogers on 8 Jan 2010 19:25
How can I show that a compact n- manifold does not embed in R^n?
From: A N Niel on 8 Jan 2010 19:38
In article
<9d430303-69b4-4fe6-954c-348f48614e57(a)s31g2000yqs.googlegroups.com>,
Maximilian Rogers <max.rogers123(a)gmail.com> wrote:

> How can I show that a compact n- manifold does not embed in R^n?

Invariance of dimension?
From: William Elliot on 9 Jan 2010 03:19
On Fri, 8 Jan 2010, Maximilian Rogers wrote:

> How can I show that a compact n- manifold does not embed in R^n?
>
Does the unit sphere S^2, embed into R^2?
From: Maximilian Rogers on 9 Jan 2010 06:34
On Jan 9, 2:19 am, William Elliot <ma...(a)rdrop.remove.com> wrote:
> On Fri, 8 Jan 2010, Maximilian Rogers wrote:
> > How can I show that a compact n- manifold does not embed in R^n?
>
> Does the unit sphere S^2, embed into R^2?

I know that the sphere doesn't embed in R^2, I wouldn't necessarily
know hoe to prove it, though...

The invariance of dimension theorem says that R^m=R^n iff m=n, right?
I am not sure how to use it to prove what i want..could you give me
more details, please?
From: William Elliot on 9 Jan 2010 07:57
On Sat, 9 Jan 2010, Maximilian Rogers wrote:
> On Jan 9, 2:19�am, William Elliot <ma...(a)rdrop.remove.com> wrote:
>> On Fri, 8 Jan 2010, Maximilian Rogers wrote:
>>> How can I show that a compact n- manifold does not embed in R^n?
>>
>> Does the unit sphere S^2, embed into R^2?
>
> I know that the sphere doesn't embed in R^2, I wouldn't necessarily
> know hoe to prove it, though...

Does the unit circle S^1, embed into R^1 ?
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