by "W. Dale Hall" <wdunderscorehallatpacbelldotnet@[EMAIL PROTECTED]
>
Apr 27, 2008 at 01:02 AM
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
