Take [0,1] with the usual topology and attach a new point y so that each neighborhood of y has open dense intersection with [0,1]. To obtain a 2nd disjoint copy, repeat the construction with [2,3] and a 2nd special point z whose neighborhoods are open and dense in [2,3]. Let A equal the union of [0,1] and z, and let B equal the union of [2,3] and y.

Singletons are closed. There exist no interesting sequences converging to y or z and thus we have a US space. Each neighborhood of A intersects B and vice versa, so this is not an AB space.

Take [0,1] with the usual topology and attach a new point y so that the neighborhoods of y are precisely those which are and open dense in [0,1]. To obtain a 2nd disjoint copy, repeat the construction with [2,3] and a 2nd special point z whose neighborhoods are precisely those which are open and dense in [2,3]. Let A equal the union of [0,1] and z, and let B equal the union of [2,3] and y.

Singletons are closed. There exist no interesting sequences converging to y or z and thus we have a US space. Each neighborhood of A intersects B and vice versa, so this is not an AB space.