Approximation of singular semialgebraic sets by smooth ones with respect to the Hausdorff metric (Q6040258)

The paper under review is concerned with approximation of singular semialgebraic sets by Nash manifolds. The authors prove that any closed semialgebraic subset of \(\mathbb{R}^n\) can be represented as a limit of Nash closed submanifolds of \(\mathbb{R}^n\) in the sense of the Hausdorff metric. Moreover, it is shown that the approximating manifolds can be realized as a semialgebraic family, that is, as fibers of a semialgebraic set in a higher dimensional Euclidean space.