SEMIALGEBRAIC SARD THEOREM FOR GENERALIZED CRITICAL VALUES

We prove that a semialgebraic differentiable mapping has a generalized critical values set of measure zero. Moreover, if the mapping is C 2 we obtain, bya generalisation of Ehresmann’s fibration theorem due to P. J. Rabier [20], a locallytrivial fibration over the complement of this set. In the complex case, we prove that the set of generalized critical values of a polynomial mapping is a proper algebraic set.

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