Subanalytic Functions
نویسنده
چکیده
We prove a strong version of rectilinearization theorem for subanalytic functions. Then we use this theorem to study the properties of arc-analytic functions.
منابع مشابه
Analytic P-adic Cell Decomposition and P-adic Integrals
Roughly speaking, the semialgebraic cell decomposition theorem for p-adic numbers describes piecewise the p-adic valuation of p-adic polyno-mials (and more generally of semialgebraic p-adic functions), the pieces being geometrically simple sets, called cells. In this paper we prove a similar cell decomposition theorem to describe piecewise the valuation of analytic functions (and more generally...
متن کاملANALYTIC p-ADIC CELL DECOMPOSITION AND INTEGRALS
We prove a conjecture of Denef on parameterized p-adic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic functions (and more generally of subanalytic functions), the pieces being geometrically simple sets, called cells. We also classify subanalytic sets up to subanalyt...
متن کاملComplements 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...
متن کاملPiecewise 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 ...
متن کاملLIPSCHITZ CONTINUITY PROPERTIES FOR p-ADIC SEMI-ALGEBRAIC AND SUBANALYTIC FUNCTIONS
We prove that a (globally) subanalytic function f : X ⊂ Qp → Qp which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken to be subanalytic. We also prove the analogous result for a subanalytic family of functions fy : Xy ⊂ Qp → Qp depending on p-adic parameters. The stat...
متن کامل