Displaying similar documents to “Whitney stratification of sets definable in the structure ”

Analytic cell decomposition of sets definable in the structure

Ta Lê Loi (1994)

Annales Polonici Mathematici

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We prove that every set definable in the structure can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.

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 be a set-germ at such that . We say that is a direction of at if there is a sequence of points tending to such that as . Let denote the set of all directions of at . Let be subanalytic set-germs at such that . We study the problem of whether the dimension of the common direction set, is preserved by bi-Lipschitz homeomorphisms. We show that although it is not true in general, it is preserved if the images of and 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.