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On the singular locus of sets definable in a quasianalytic structure
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Krzysztof Jan Nowak
Published/Copyright:
October 1, 2013
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.
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Keywords for this article
Quasi-subanalytic functions and sets;
singular locus;
uniformisation;
Gateaux differentials;
Puiseux’s theorem with parameter;
composite function theorem
Articles in the same Issue
- Masthead
- Some remarks on Nijenhuis brackets, formality, and Kähler manifolds
- Semifields from skew polynomial rings
- A note on CR quaternionic maps
- On maximal curves of Fermat type
- On the singular locus of sets definable in a quasianalytic structure
- A product integral representation of mixed volumes of two convex bodies
- The Tutte polynomial of the Sierpiński and Hanoi graphs
- A lower bound for the Ricci curvature of submanifolds in generalized Sasakian space forms
- The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
- Inscribable stacked polytopes
- Differential Harnack estimates for backward heat equations with potentials under an extended Ricci flow
