Analytic cell decomposition of sets definable in the structure
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.
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Ta Lê Loi (1994)
Annales Polonici Mathematici
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.
P. Schapira (1988/1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
Riccardo Benedetti, Masahiro Shiota (1991)
Mathematische Zeitschrift
Adam Parusiński (1994)
Annales scientifiques de l'École Normale Supérieure
Tadeusz Mostowski (2004)
Banach Center Publications
François Loeser (1990/1991)
Séminaire Bourbaki
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov (2013)
Journal of the European Mathematical Society
A coordinate cone in is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...
A. B. Cabello, Z. Hajto (1995)
Revista Matemática de la Universidad Complutense de Madrid
A first part of a systematic presentation of Pfaffian geometry is given.
Stanislas Łojasiewicz (1993)
Annales de l'institut Fourier
Bernard Teissier (1989)
Publications Mathématiques de l'IHÉS
Masahiro Shiota (1988)
Banach Center Publications
Ta Loi (1996)
Banach Center Publications
The aim of this paper is to prove that every subset of definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).
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