Cassidy, Phan and Shelton associate to any regular cell complex X a quadratic
K-algebra R(X). They give a combinatorial solution to the question of when this
algebra is Koszul. The algebra R(X) is a combinatorial invariant but not a
topological invariant. We show that nevertheless, the property that R(x) be
Koszul is a topological invariant.

In the process we establish some conditions on the types of local singular-
ities that can occur in cell complexes X such that R(X) is Koszul, and more
generally in cell complexes that are pure and connected by codimension one
faces.