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Aug 31, 2014 at 17:38 comment added Yemon Choi @LeonelRobert that seems to be correct - thanks. The description feels somehow "non-canonical", since there are lots of ways to chop up the rationals to run the same argument, but maybe that just illustrates the large automorphism group of this space
Aug 31, 2014 at 16:23 comment added Leonel Robert The ideal of $A$ of functions supported in $[N,N+1)$ is isomorphic to $\ell_\infty(\mathbb N)$, and $A$ seems to be a direct sum of all these (in the category of C*-algebras). So $\Omega_S$ should be the one point compactification of a countable union of copies of $\beta N$.
Aug 31, 2014 at 12:54 history edited Yemon Choi CC BY-SA 3.0
added full stop before someone else does
Aug 31, 2014 at 12:33 history asked Yemon Choi CC BY-SA 3.0