For a space , a function such that each is called an open neighborhood assignment (ONA). is a -space if for each ONA, , there exists a closed discrete such that . For an ONA and , is said to be -sticky if is closed discrete and whenever . Among other results, it is proved that
(1) Box products of scattered spaces of height 1 are -spaces,
(2) A subspace of a linearly ordered space is a -space iff it has no closed stationary subset (a harder proof of this result is due to van Douwen),
(3) A subspace of the product of finitely many ordinals is a -space iff it is metacompact iff it has no closed stationary subsets.