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Re: [Phys-l] cosmology




On 09/09/2007 at 12:00 PM, someone wrote:

As for what "closed" properly means in cosmology, I have
no idea. I know what it means in mathematics, i.e. closed
sets and open sets

The use in cosmology comes from differential topology instead of general
topology. A closed manifold is one that is compact without boundary. A sphere
is closed, Euclidean space is open (noncompact without boundary), and a solid
ball is compact with a boundary (the spherical surface).

That's why a closed universe is both time- and space-limited.

The FLRW models come with infinite (noncompact) time but either compact or
noncompact space, and two kinds of the last. The 3 cases are frequently
shorthanded in the literature as k = +1, 0, -1, respectively: spherical, flat,
or hyperbolic space.

The latest evidence is that space is hyperbolic.

--
Phil Parker
--------------------------------------------
URL http://www.math.wichita.edu/~pparker/
Random quote:
Saint, n. A dead sinner revised and edited.
---Ambrose Bierce, "The Devil's Dictionary"