🚀 go-pugleaf

pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

> What I don't understand here is how "living in R^n" is of itself
> creating complexity and obscurity.  I can see that the
> arbitrariness of f might get in the way.  But where does the
> complexity and obscurity creep in if for example we define a
> manifold to be a smooth retract of an open subset of R^n?

The choice of ambient space is also somewhat arbitrary.  If the
manifold can be imbedded in R^n, then it can also be imbedded in
R^{n+1}, to say nothing of imbeddings in other manifolds.  The point
is that manifolds exists independently of their imbeddings in R^n or
other manifolds.  Any reasonable definition should possess this
invariance.

Steven Smith