  From N-tensor powers of the Toeplitz algebra, we construct a multipullback
C*-algebra that is a noncommutative deformation of the complex projective space
CP(N). Using Birkhoff's Representation Theorem, we prove that the lattice of
kernels of the canonical projections on components of the multipullback
C*-algebra is free. This shows that our deformation preserves the freeness of
the lattice of subsets generated by the affine covering of the complex
projective space.
