Real Algebraic and Analytic Geometry

Preprint Server

Previous   Next
195. Nicolas Dutertre:
Semi-algebraic neighborhoods of closed semi-algebraic sets.


Submission: 2006, February 13.

Given a closed (not necessarily compact) semi-algebraic set $X$ in $\mathbb{R}^n$, we construct a nonnegative semi-algebraic $C^2$ function $f$ such that $X=f^{-1}(0)$ and such that for $\delta > 0$ sufficiently small, the inclusion $X \subset f^{-1}([0,\delta])$ is a retraction. As a corollary, we obtain several formulas for $\chi(X)$.

Mathematics Subject Classification (2000): 14P10, 14P25.

Full text, 23p.: dvi 111k, ps.gz 204k, pdf 261k.

Server Home Page