  The "polyhedral product functor" produces a space from a simplicial complex L
and a collection of pairs of spaces, {(A(i),B(i))}, where i ranges over the
vertex set of L. We give necessary and sufficient conditions for the resulting
space to be aspherical. There are two similar constructions, each of which
starts with a space X and a collection of subspaces, {X_i} and then produces a
new space. We give conditions for the results of these constructions to be
aspherical. All three techniques can be used to produce examples of closed
aspherical manifolds.
  Abstract for Corrigenda: This note concerns two refinements to the earlier
work by the first author. First, when L is infinite, the definition of
polyhedral product needs clarification. Second, the earlier paper omitted some
subtle parts of the necessary and sufficient conditions for polyhedral products
to be aspherical. Correct versions of these necessary and sufficient conditions
are given in the present paper.
