On the singular locus of sets definable in a quasianalytic structure
نویسنده
چکیده
Given a quasianalytic structure, we prove that the singular locus of a quasi-subanalytic set E is a closed quasi-subanalytic subset of E. We rely on some stabilization effects linked to Gateaux differentiability and formally composite functions. An essential ingredient of the proof is a quasianalytic version of Glaeser’s composite function theorem, presented in our previous paper.
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