by Mike <mjake@[EMAIL PROTECTED]
>
Apr 27, 2008 at 05:55 AM
On Apr 27, 4:02=A0am, "W. Dale Hall"
<wdunderscorehallatpacbelldotnet@[EMAIL PROTECTED]
> wrote:
> Mike wrote:
> > Are there metric space or otherwise manifolds that are not locally
> > Euclidean? Thanks.
>
> If you mean "locally homeomorphic to Euclidean space",
> meaning that every point has a neighborhood homeomorphic
> to an open subset of R^n for some n, take the space
> formed by taking three rays meeting at the origin in R^2.
>
> No neighborhood of the origin in this space is homeomorphic
> to an open subset of R^n for any n.
>
> More pathological examples can be constructed (such as
> spaces for which no point has a neighborhood homeomorphic
> to an open subset of R^n), of course.
>
> Dale
I guess what I mean is that the basis vectors at a point in some
coordinate system are not orthogonal to each other as they are in
local euclidean coordinate systems? Or is it that ANY coordinate
system can be parameterized locally with euclidean geometry? Thanks.
