Real Algebraic and Analytic Geometry

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313. Krzysztof Jan Nowak:
On the singular locus of sets definable in a quasianalytic structure.


Submission: 2012, February 3.

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 paper~\cite{Now4}.

Mathematics Subject Classification (2010): 14P15, 32B20.

Keywords and Phrases: quasi-subanalytic sets and functions, Gateaux differentials, composite function theorem.

Full text, 17p.: dvi 60k, pdf 299k.

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