Massimo Ferrarotti

Local algebraic approximation of semianalytic sets

Abstract. Two subanalytic subsets of Rn are called s-equivalent at a common point P if the Hausdorff distance between their intersections with the sphere centered at P of radius r vanishes to order > s when r tends to 0. In this paper we prove that every s-equivalence class of a closed semianalytic set contains a semialgebraic representative of the same dimension. In other words any semianalytic set can be locally approximated of any order s by means of a semialgebraic set and hence, by previous results, also by means of an algebraic one

Algebraic approximation of germs of real analytic sets

Two subanalytic subsets of ℝ n are s-equivalent at a common point, say O, if the Hausdorff distance between their intersections with the sphere centered at O of radius r goes to zero faster than r s . In the present paper we investigate the existence of an algebraic representative in every s-equivalence class of subanalytic sets. First we prove that such a result holds for the zero-set V(f) of an analytic map f when the regular points of f are dense in V(f). Moreover we present some results concerning the algebraic approximation of the image of a real analytic map f under the hypothesis that f ―1 (O) = {O} . .

Volume on stratified sets

SummaryIn this paper a notion of volume on closed stratified subsets of a riemannian manifold M is defined and the following results are proved:1)There are compact 2-dimensional stratified suvsets of R3which satisfy strict Whitney condition and have not finite volume.2)If a closed p-dimensional stratified subset of M satisfies Whitney condition and has strata in dimension p and p — 1 only, then it has locally finite volume.3)Subanalytic sets have locally finite volume.

Regular differential forms on stratified spaces

AbstractGiven a stratified space W, we present for each perversity

Generalized Hestenes’ Lemma and extension of functions

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Real algebraic varieties with prescribed tangent cones

a complex of differential forms which are defined on any stratum, are “regular” with respect to a fixed family of trivializations of W and whose cohomology is dual to the intersection homology of W for the complementary perversity

Some results about integration on regular stratified sets

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