Subanalytic sets and feedback control

Rigid Subanalytic Sets

Let K be an algebraically closed field endowed with a complete non-archimedean norm. Let f : Y → X be a map of K-affinoid varieties. In this paper we study the analytic structure of the image f(Y ) ⊂ X; such an image is a typical example of a subanalytic set. We show that the subanalytic sets are precisely the D-semianalytic sets, where D is the truncated division function first introduced by D...

On the Normal Cycles of Subanalytic Sets

We present a short proof of the existence of the normal cycle of a compact subanalytic set. The approach is inspired by some old ides of Joseph Fu, uses Morse theoretic techniques and o-minimal topology.

One-Dimensional Fibers of Rigid Subanalytic Sets

Let K be an algebraically closed eld of any characteristic, complete with respect to the non-trivial ultrametric absolute value jj : K ! R +. By R denote the valuation ring of K, and by } its maximal ideal. We work within the class of subanalytic sets deened in L2], but our results here also hold for the strongly subanalytic sets introduced in S] as well as for those subanalytic sets considered...

Uniform Properties of Rigid Subanalytic Sets

In the context of rigid analytic spaces over a non-Archimedean valued field, a rigid subanalytic set is a Boolean combination of images of rigid analytic maps. We give an analytic quantifier elimination theorem for (complete) algebraically closed valued fields that is independent of the field; in particular, the analytic quantifier elimination is independent of the valued field’s characteristic...

RECTILINEARIZATION AND UNIFORMIZATION OF k-SUBANALYTIC SETS AND FUNCTIONS