We give rather simple answers to two long-standing questions in real-analytic geometry, on global smoothing of a subanalytic set, and on transformation of a proper real-analytic mapping to a mapping with equidimensional fibers by global blowings-up of the target. These questions are related: a positive answer to the second can be used to reduce the first to the simpler semianalytic case. We show that the second question has a negative answer, in general, and that the first problem nevertheless has a positive solution.
"Global smoothing of a subanalytic set." Duke Math. J. 167 (16) 3115 - 3128, 1 November 2018. https://doi.org/10.1215/00127094-2018-0032