Re: universe: finite/infinite, closed/open

[John Denker <jsd@MONMOUTH.COM>]

At 02:13 PM 8/11/00 -0600, Jim Green wrote:
> > Whether
> >the universe is finite or infinite in size, in principle depends
> >fundamentally on whether it is open or closed.
>
> Is there agreement here on the above?

I think the quoted statement is trivial, because astronomers *define* open
and closed to mean infinite and non-infinite respectively.  (There's
nothing "fundamental" or "in principle" about it.)

Obviously astronomers are not using closed and open in the mathematical
sense;  see
  http://noisefactory.co.uk/research/sci-math/topology/index.html
for the mathematical definitions.  This is obvious because the mathematical
definitions necessarily speak of subsets that are "closed in X" or "open in
X" with reference to some definite universal set X.  The universal set X is
always closed in X *and* open in X.  So topologically speaking it would be
silly to try to draw a distinction between an open universe and a closed
universe.

Maybe we should call the math police and force the astronomers to use the
correct technical terms.
  -- To describe a finite universe, the best approach would be to call it
a "finite universe".
  -- To describe an infinite universe, the best approach would be to call
it an "infinite universe".  Duh.

If astronomers still have a craving for fancy topological terminology, the
terms "compact" and "noncompact" might come in handy.