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

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

master1729

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More options Nov 7 2009, 12:07 pm

Newsgroups: sci.math

From: master1729 <tommy1...@gmail.com>

Date: Sat, 07 Nov 2009 07:07:17 EST

Local: Sat, Nov 7 2009 12:07 pm

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

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G.A. Edgar wrote :

> In article
> <808290445.28584.1257559402748.JavaMail.r...@gallium.m
> athforum.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/

indeed.

tommy1729

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