AElysium spins, like a wheel, and the resulting centrifugal force creates artificial gravity on its inner edge. This keeps both its inhabitants and the atmosphere effectively pinned down to the surface. It's an old concept for a practical way to achieve artificial gravity in space.
AOxygen in Elysium's atmosphere could be maintained by plant photosynthesis converting exhaled CO2 to oxygen. The bigger problem is that atmosphere could not be retained without some kind of "force field", like we see the "bad guy" using twice to defend against Max's weapon fire. Now, for some reason, they never show us Elysium rotating in any of the scenes. But assuming that it did rotate to generate an artificial standard Earth gravity, "artificial gravity" COULD NOT retain the atmosphere! Nor could it produce anything close to normal air pressure! Without a magic force field, the atmosphere would be lost very quickly for many reasons. Brownian motion alone would be enough to continuously kick molecules of air up and over the lip of the station. Once over the lip, centripetal force would fling the air molecules out into space, lost forever. Note: This doesn't happen on Earth, because real gravity pulls atmosphere back, no matter where it goes. Unless it's moving faster than the Earth escape velocity of 11km/sec, which is really fast! A bigger problem is that gravity isn't what creates atmospheric pressure: It's the weight of air above. That's why the air is so thin on top of Mount Everest, even though the force of gravity is nearly the same as the gravity at sea level (G=9.8 vs 9.7)
