Global smoothing of a subanalytic set (Q1626391)

The authors give a positive solution to the long-standing problem of global smoothing of subanalytic sets (embedded and nonembedded). Also an analogous semialgebraic version is provided. The related question of whether a proper real analytic mapping admits a transformation to a mapping with locally equidimensional fibers by global blowing-ups of the target space is shown to have a negative answer in general. A similar construction is used to show that in the real analytic category a composite of blowing-ups is not always also a blowing-up.