Riemann space

[Ray Easton]

On Tuesday, Nov 28, 2006, at 12:02 US/Central, Ya Sam wrote:

> Thanks for this attempt! Have to confess it is still kinda foggy to me.
>
> So the laws of Euclidian space will work locally and not globally?
>
> I've read that some Euclid's notions do not hold in Riemann space, 
> like there are no parallel lines there...

A "Riemann space" is, depending upon whom one asks, either simply 
another name for  a metric space, or, more usually, a space which is 
everywhere locally Euclidean.  Of course, Euclidean space is itself a 
"Riemann space" in this sense, and it (obviously!) obeys the laws of 
Euclidean space both locally and globally.

Perhaps what you have in mind as a "Riemann space" is a two-dimensional 
space with Riemannian geometry -- such as the surface of a sphere.  Or 
maybe some generalization of this to higher dimensions.