Journal of the
Korean Mathematical Society JKMS

Let $G$ be a compact semialgebraic group and $M$ a semialgebraic $G$-set. We prove that there exists a semialgebraic slice at every point of $M$. Moreover $M$ can be covered by finitely many semialgebraic $G$-tubes. As an application we give a different proof that every semialgebraic $G$-set admits a semialgebraic $G$-embedding into some semialgebraic orthogonal representation space of $G$, which has been proved in [15].

Keywords: transformation groups, semialgebraic, slice, embedding

MSC numbers: 57Sxx, 14P10, 57S99, 57Q35