  The set of chambers of a real hyperplane arrangement may be ordered by
separation from some fixed chamber. When this poset is a lattice, Bjorner,
Edelman, and Ziegler proved that the chambers are in natural bijection with the
biconvex sets of the arrangement. Two families of examples of arrangements with
a lattice of chambers are simplicial and supersolvable arrangements. For these
arrangements, we prove that the chambers correspond to biclosed sets, a
weakening of the biconvex property.
