Context for Question
The colonisation of the planet [ INSERT NAME ] was an enormous social experiment performed by the Terran Planetary Science and Terraforming Council; this previously-barren world had its orbit and gravity adjusted to suit human requirements, but was uniquely terraformed so as to create an ecumenopolis (much like Coruscant of the Star Wars universe).
Any criminals placed on death row within the justice systems of other human-colonised worlds instead had their memories irrevocably wiped, any diseases cured, scars healed (including missing limbs) and tattoos removed, and were sent to become the founding citizens of the societies on this planet. The purpose of this exercise was to test the sustainability of a planet-wide society developing without the natural world (including all plants and most animals, and fungi).
Their food was to be entirely vat-grown, using animal and some plant tissues, but that was the most they would ever see of either type of organism. Their language and the visual aspects of their culture would be expressed through small and large digital screens; if you were to give any of these people a piece of paper and a pencil or pen, they would not only not know how to use it, but they could not tell you what it was made from. They had never experienced actual plant fibres or extracts.
Now, the Question:
How does this society produce its oxygen? The nearest plants need to be on another planet (for the purposes of this social experiment), so is there some other artificial chemical process which could be used to extract O2 from CO2? Further, could these filter materials be periodically 'cleaned' (if you will), even if they might eventually run out of cycles? And when this happens, could they be recycled?
Also, I just want to specify that the memory wipes of the citizens are completely irreversible. I am not concerned about the ethics or reliability of this procedure for the moment.
EDIT 1: I would also like to point out that, at the point where the narrative is set, the number of local years (of that planet) since the first colonists arrived is between 300 and 500, with the number of days in these periods similar to that of Earth. A few generations have existed and died, and the population has spread out further among the pre-made skyscrapers of the ecumenopolis. (Also, the genetic diversity of the population is maintained by either the government or a scientific body.)
EDIT 2: These people need to be able to walk around the planet as we do (without pressure suits or gas masks). I am also assuming that water is kept in a large (yes, ocean-sized) reservoir on a local moon, and brought down to be used and recycled for a few years, before returning to the moon and being replaced.
EDIT 3: For the world of this narrative, normally I would place water reservoirs underground, but I wanted to make it clear to everyone here that ocean organisms and any solution involving large bodies of water were not a viable option. So, yes, I sent them to the moon. I can see how this would look in retrospect, and I'm sorry about that. I just didn't need solutions involving the planet's non-existent oceans, or any solution too reliant on a large body of water.