Chains of points in the Semple tower

We introduce a proximity relation in the Semple tower over a nonsingular algebraic variety Z, and we prove a formula, relating the multiplicity of a curve C in Z at a point z with the multiplicities of its iterated Nash blowing-ups at the proximate points of z, parallel to a classical formula of Enriques. We also show that the Semple tower of a surface parametrizes its infinitely near points.