I have long thought about how to solves this problem with my cats. I currently have a two-door setup (analogous to an airlock) and this is not a problem. Nevert

I have long thought about how to solves this problem with my cats. I currently have a two-door setup (analogous to an airlock) and this is not a problem. Nevertheless, what I try is to teach them that anytime I open a door which was previously closed, they have to first sit and then wait for me to give them permission (I say a specific word) before they are allowed to pass through it. Until then they must be seated. Sometimes I open the door, go to the other side and do my stuff and get back and don't let them through. This also lets them know that they don't _always_ get to go through that door. If I see them make the first small movement as if to get up, a stern "hey" makes them drop that idea. Of course, there is no risk _now_ as they can't go outside from the 2-door arrangement but I may move to a different house some time in the future and that might be set up differently. Also in general, I don't want them to have a habit of running through doors that just opened.