🚀 go-pugleaf

asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:

>As has been mentioned, it *is* a theorem that all manifolds do occur
>as subspaces of some Euclidean space: in fact, any n-manifold embeds in R^(2n).
>
>This is a pleasant theorem, but it would be inappropriate to take this as a 
>definition.

What about the one-dimensional helix embedded in R^3. Is the helix not a
1-manifold? Note that if you compact it along its axis you get a circle
(also a 1-manifold--is this S^1?) embedded in R^2. But a circle is a
degenerate case of a helix ("stretching" along the axis having vanished)
and is not in general a helix.

Someone educate me on this.

Gruss,
Dr Bruce Scott                             The deadliest bullshit is
Max-Planck-Institut fuer Plasmaphysik       odorless and transparent
bds at spl6n1.aug.ipp-garching.mpg.de                 -- W Gibson


--
   The opinions expressed are not necessarily those of the University of
     North Carolina at Chapel Hill, the Campus Office for Information
        Technology, or the Experimental Bulletin Board Service.
           internet:  laUNChpad.unc.edu or 152.2.22.80