In article
<c9362ebd-5844-4a15-866c-bae56fa09f38@[EMAIL PROTECTED]
>,
Mike <mjake@[EMAIL PROTECTED]
> wrote:
> On Apr 27, 4:02 am, "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.
You asked about a metric space, which doesn't need to have any
coordinate system. Try t make your question more precise.
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