  We study a notion of dimension which was introduced by R. Heitmann in his
remarkable paper in 1984, and also a related notion, implicit in the proofs in
his paper. We develop these notions in the general framework of distributive
lattices and spectral spaces. We obtain in this way constructive versions of
important theorems in commutative algebra, with simpler proofs than the
classical ones, and some new results.
