  The complement of an arrangement A of a finite number of affine hyperplanes
in complex n-space has the structure of a poset of spaces indexed by the
intersection poset, L(A). The space corresponding to G in L(A) is homotopy
equivalent to the complement of the hyperplanes in the central arrangement A_G
normal to G. This poset of spaces structure can be used to repair a spectral
sequence argument in two earlier papers of Davis, Januszkiewicz, Leary and Okun
for computing certain cohomology groups of arrangement complements. Similarly,
toric hyperplane arrangements have the structure of a diagram of spaces and
this structure can be used fix a spectral sequence argument in an earlier paper
of Davis and Settepanella.
