I want to create a system to flush carbon dioxide from air. Why? I do have a good reason.
"Stuffiness," the sensation commonly found in enclosed rooms with no air circulation, is almost assuredly a carbon dioxide buildup symptom. The air feels oppressive and stale, and one has an immediate urge to try to open a window. One feels drowsy and irritated, and everything smells bad. I know this because as a small child, I used to like to hide under blankets, which would become stuffy in short order, to the point where I started to associate hot air with stuffy and cold air with fresh. The stuffiness was due to poor air circulation: the carbon dioxide of my breath would build up until I exited the blanket.
NASA probably knows a few ways to do this, as it became critically important on space missions. You only have the air you bring with you in space, so it is critical to keep it as fresh as physically possible. Drowsy, confused, astronauts poisoned by their own breath is a bad thing. Their technique involves a rather complicated membrane system performed under pressure.
If I were to invent my own system, I think I would work with the chemical properties of carbon dioxide itself. I can extract it by cooling it off -- carbon dioxide sublimates long long before oxygen precipitates into a liquid. I can extract it with pressure, bringing the carbon dioxide into its liquid state and siphoning it off. I could even extract it with chemical combinations, like Sodium or Potassium Hydroxide, which tend to absorb carbon dioxide until they reach a saturation point, but I'd want an industrial type technique that I could set up and not have to personally fuss with afterwards.
Having installed one of these systems in a house, stuffiness is banished forever. What to do with the carbon dioxide? I can shunt it out of the house, thus getting all the benefits of opening a window without losing all my heating, which is sweet, but for even better works, I can use it as the security system for a greenhouse. The greenhouse is, when no humans are expected inside, flooded with all the carbon dioxide from the house. All pests die. Any intruder dies. It's just plants and a few bacteria, with the plants slowly reoxygenating the place.