Displaying similar documents to “Whitney stratification of sets definable in the structure e x p

On semialgebraic points of definable sets

Artur Piękosz (1998)

Banach Center Publications

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We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o-minimal structure with analytic cell decomposition are definable. Moreover, the operation of taking semialgebraic points is idempotent and the degree of complexity of semialgebraic points is bounded.

Constructible functions on 2-dimensional analytic manifolds.

Isabelle Bonnard, Federica Pieroni (2004)

Revista Matemática Complutense

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We present a characterization of sums of signs of global analytic functions on a real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on M if and only if this is true on each compact subset of M. This characterization gives a necessary and sufficient condition for an analytically constructible function, i.e. a linear combination with integer coefficients of Euler characteristic of fibers of proper...

The directional dimension of subanalytic sets is invariant under bi-Lipschitz homeomorphisms

Satoshi Koike, Laurentiu Paunescu (2009)

Annales de l’institut Fourier

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Let A n be a set-germ at 0 n such that 0 A ¯ . We say that r S n - 1 is a direction of A at 0 n if there is a sequence of points { x i } A { 0 } tending to 0 n such that x i x i r as i . Let D ( A ) denote the set of all directions of A at 0 n . Let A , B n be subanalytic set-germs at 0 n such that 0 A ¯ B ¯ . We study the problem of whether the dimension of the common direction set, dim ( D ( A ) D ( B ) ) is preserved by bi-Lipschitz homeomorphisms. We show that although it is not true in general, it is preserved if the images of A and B are also subanalytic....

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).

Intersection theory in complex analytic geometry

Piotr Tworzewski (1995)

Annales Polonici Mathematici

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We present a construction of an intersection product of arbitrary complex analytic cycles based on a pointwise defined intersection multiplicity.