Real Algebraic and Analytic Geometry |

Semi-algebraic neighborhoods of closed semi-algebraic sets.

e-mail:

Submission: 2006, February 13.

*Abstract:
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