SEMI-ALGEBRAIC GEOMETRY WITH RATIONAL CONTINUOUS FUNCTIONS

Jean-Philippe Monnier (1)

1 Service archéologique

Let X be a real algebraic subset of R n. We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational continuous functions on X. We also study the integral closure of some rings of rational continuous functions on X.

Mots clés: regular function; regulous function; rational function; real algebraic variety; alge-braically constructible function; semi-algebraic set

Domaines: Géométrie algébrique [math.AG]

Jean-Philippe Monnier. SEMI-ALGEBRAIC GEOMETRY WITH RATIONAL CONTINUOUS FUNCTIONS. 2016. ⟨hal-01286990v1⟩