Uniform radius and regular stratifications

TL;DR

This paper explores how germs of real functions with isolated singularities deform within various tame categories, analyzing their stratifications and the effects of these deformations across different mathematical structures.

Contribution

It provides a detailed study of deformations of germs of isolated singularities in various tame categories and their impact on natural stratifications.

Findings

Deformations of germs can be characterized within tame categories.

Stratifications are preserved or transformed under specific deformations.

The work links singularity theory with tame geometric structures.

Abstract

In this paper we investigate how germs of real functions can change under deformation. In particular we look at deformations of germs of isolated singularities from R_n to R_k (n >= k) and the relation with there natural stratification in some tame categorie (algebraic, analytic, semi-algebraic, subanalytic, o-minimal straucture polynomially bounded). The word tame in this paper will refer to one of these categories.