Difference between R^n and Euclidean n-space? - sci.math

Message from discussion Difference between R^n and Euclidean n-space?

G. A. Edgar

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More options Nov 7 2009, 10:56 am

Newsgroups: sci.math

From: "G. A. Edgar" <ed...@math.ohio-state.edu.invalid>

Date: Sat, 07 Nov 2009 05:56:16 -0500

Local: Sat, Nov 7 2009 10:56 am

Subject: Re: Difference between R^n and Euclidean n-space?

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<808290445.28584.1257559402748.JavaMail.r...@gallium.mathforum.org>,

Bacle <ba...@yahoo.com> wrote:
> Hi, everyone:

> I have seen authors like John Lee in his "Smooth Manifolds" book, use
> these two terms as being different, but without , AFAIK, explaining the
> difference between the two.

> I assume it may be that Euclidean n-space is the manifold R^n with a
> preferred , or "default" chart, but I am not sure of this.

> Anyone Else Know.?.

> Thanks In Advance.

I would probably say that R^n is Euclidean n-space together with a
coodinate system. Euclidean n-space has no preferred point "the
origin" nor preferred directions for the coordinate planes, while R^n
has all of those.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

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