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Abstract
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 stabilisation 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.
Keywords: Quasi-subanalytic functions and sets; singular locus; uniformisation; Gateaux differentials; Puiseux’s theorem with parameter; composite function theorem
Published Online: 2013-10-01
Published in Print: 2013-10
© 2013 by Walter de Gruyter GmbH & Co.