Publication: Semialgebraic and semianalytic sets
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Publication Date
1991
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Institut Henri Poincaré
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Abstract
In this talk I shall discuss the notion and some basic features of semialgebraic and semianalytic sets, which are one main concern of Real Geometry
Description
Papers from the seminar held at the Institut Henri Poincaré, Paris, March 14, 1990
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Citation
Lojasiewicz S. : Ensembles semianalytiques, I.H.E.S. (prépublication) (1964).
Bochnak J., Coste M., Roy M.-F.: Géométrie algébrique réelle. Berlin, Heidelberg, New York, Springer (1987).
Bröcker L.: Minimale Erzeugung von Positivbereich. Geom. Dedicate 16, 335-350 (1984).
Scheiderer C. : Stability index of real varieties. Invent. Math. 97, 467-483 (1989).
Bröcker L. : On basic semialgebraic sets. To apperar in Geom. Dedicata. Concerning the semianalytic case, Lojasiewicz's Lecture Notes quoted above is again the classical reference for local results. The global ones have appeared in the following papers
Ruiz J. : On Hilbert's 17th problem an real Nullstellensatz for global analytic functions. Math. Z. 190, 447-459 (1985).
Andradas C., Bröcker L., Ruiz R. : Minimal generation of basic open semianalytic sets. Invent. Math. 92, 409-430 (1988).
Ruiz J. : On the connected components of a global semianalytic set. Journal Reine Angew. Math. 392, 137-144 (1988).
Ruiz J. : On the topology of global semianalytic sets. In Real analytic and algebraic geometry, Proc. Trento 1988, M. Galbiati, A. Tognoli (Eds.) Springer-Verlag LNM 1420, 237-246. Finally, there is an abstract theory of real constructible sets that generalizes both the algebraic and the analytic cases. A symmetric presentation of it is the subject of the forthcoming book.
Andradas C., Bröcker L., Ruiz J., Real constructible sets.