Subanalytic

$X\subseteq\Bbb{R}^n$ is subanalytic if, for all $x\in\Bbb{R}^n$, there is an open $U$ and $Y\subset\Bbb{R}^{n+m}$ a bounded Semianalytic set such that $X\cap U$ is the projection of $Y$ into $U$.

See also Semianalytic

References

Bierstone, E. and Milman, P. ``Semialgebraic and Subanalytic Sets.'' IHES Pub. Math. 67, 5-42, 1988.

Marker, D. ``Model Theory and Exponentiation.'' Not. Amer. Math. Soc. 43, 753-759, 1996.