X≠0, y≠0, if the coordinate axis is removed, any two points in different quadrants cannot be connected by a polyline whose points all belong to the set, so it is not an open area.

(x，y) 1 < x？ +y？ ≤2﹜ Nothing, an open region must be an open set first, but a closed region must be a closed set first. Obviously, this set is neither open nor closed.