Constructible functions on 2-dimensional analytic manifolds.

Isabelle Bonnard; Federica Pieroni

Displaying similar documents to “Constructible functions on 2-dimensional analytic manifolds.”

An arc-analytic function with nondiscrete singular set

Krzysztof Kurdyka (1994)

Annales Polonici Mathematici

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We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².

A counterexample to subanalyticity of an arc-analytic function

Krzysztof Kurdyka (1991)

Annales Polonici Mathematici

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We construct an arc-analytic function (i.e. a function analytic on each analytic arc) whose graph is not subanalytic.

Whitney stratification of sets definable in the structure $ℝ_{e x p}$

Ta Loi (1996)

Banach Center Publications

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The aim of this paper is to prove that every subset of $ℝ^{n}$ definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).

Improper intersection of analytic curves.

Krasiński, Tadeusz (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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On the intersection product of analytic cycles

Sławomir Rams (2000)

Annales Polonici Mathematici

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We prove that the generalized index of intersection of an analytic set with a closed submanifold (Thm. 4.3) and the intersection product of analytic cycles (Thm. 5.4), which are defined in [T₂], are intrinsic. We define the intersection product of analytic cycles on a reduced analytic space (Def. 5.8) and prove a relation of its degree and the exponent of proper separation (Thm. 6.3).

Analytic cell decomposition of sets definable in the structure $ℝ_{e x p}$

Ta Lê Loi (1994)

Annales Polonici Mathematici

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We prove that every set definable in the structure $ℝ_{e x p}$ can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.