  Let X be a smooth simplicial toric variety. Let Z be the set of T-fixed
points of X. We construct a filtration for A(Z), the ring of complex-valued
functions on Z, such that Gr A(Z) is isomorphic to the cohomology algebra of X.
This is the explanation of the general results of Carrell and Liebermann on the
cohomology of T-varities, in the case of toric varieties. We give an explicit
isomorphism between Gr A(Z) and Brion's description of the polytope algebra.
