GLOBAL ALMOST ANALYTIC ALGEBRAICITY OF ANALYTIC SETS

Let X be a nonsingular real algebraic subset of Rn. There are known several results concerning analytic subsets of X which are analytically or Cr equivalent to algebraic sets, i.e., which can be transformed by an analytic or Cr diffeomorphism, r = 0, 1, 2, …, of X onto algebraic subsets. In general, Cr equivalence does not imply analytic equivalence, however, we show in this paper that Cr equivalence often can be replaced by, much stronger, "almost analytic" equivalence. © 1990 by Pacific Journal of Mathematics.