My room has been traditionally Penwiper's stalking ground, metaphorically speaking, especially my bed. (She likes to watch television.) Either cat is allowed in here, though, and Pandora hides in my closet a lot. (It has lots of semi-open boxes for her to crawl into.) Both cats know how to open the door from the other side if it is not securely latched (headbutting and pulling with front paws in that order).
Just now, I heard the creak of my door while almost napping (Vicodin for my foot and the aftereffects of a flu shot can do that). When I got up, Pandora had come in, pushed the door shut securely behind her, presumably by headbutting it, and sat down in front of the closed door.
No. I refuse to have a turf war in my room.