A Thom Isotopy Theorem for nonproper semialgebraic maps

We prove a version of the Thom Isotopy Theorem for nonproper semialgebraic maps $f\text{\hspace{0.17em}⁣}:X\to {\mathbb{R}}^m$, where $X\subset {\mathbb{R}}^n$ is a semialgebraic set and $f$ is the restriction to $X$ of a smooth semialgebraic map $F:{\mathbb{R}}^n\to {\mathbb{R}}^m$.