  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 fibres 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.
