Subanalytic blow-$\mathcal {C}^m$ functions

Subanalytic Functions

We prove a strong version of rectilinearization theorem for subanalytic functions. Then we use this theorem to study the properties of arc-analytic functions.

Piecewise Linearization of Real-valued Subanalytic Functions

We show that for a subanalytic function / on a locally compact subanalytic set X there exists a unique subanalytic triangulation (a simplicial complex K , a subanalytic homeomorphism n: \K\ —► X) such that f o n\a , a 6 K , are linear. Let X be a subanalytic set contained and closed in a Euclidean space. A subanalytic triangulation of X is a pair (K , n) where K isa simplicial complex and n is ...

RECTILINEARIZATION AND UNIFORMIZATION OF k-SUBANALYTIC SETS AND FUNCTIONS

A nonsmooth Morse-Sard theorem for subanalytic functions

According to the Morse-Sard theorem, any sufficiently smooth function on a Euclidean space remains constant along any arc of critical points. We prove here a theorem of Morse-Sard type suitable as a tool in variational analysis: we broaden the definition of a critical point to the standard notion in nonsmooth optimization, while we restrict the functions under consideration to be semi-algebraic...

Complements of Subanalytic Sets and Existential Formulas for Analytic Functions

We show that the complement of a subanalytic set defined by real analytic functions from any subalgebra closed under differentiation is a subanalytic set defined by the functions from the same subalgebra. This result has an equivalent formulation in logic: Consider an expression built from functions as above using equalities and inequalities as well as existential and universal quantifiers. Suc...