Publication: On globally defined semianalytic sets
Loading...
Full text at PDC
Publication Date
2015-12-17
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Citations
Exportar
Abstract
In this work we present the concept of C-semianalytic subset of a real analytic manifold and more generally of a real analytic space. C-semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analytic sets introduced by Cartan (C-analytic sets for short). More precisely S is a C-semianalytic subset of a real analytic space (X, OX ) if each point of X has a neighborhood U such that S ∩ U is a finite boolean combinations of global analytic equalities and strict inequalities on X. By means of paracompactness C-emianalytic sets are the locally finite unions of finite boolean combinations of global analytic equalities and strict inequalities on X. The family of C-semianalytic sets is closed.
Description
UCM subjects
Unesco subjects
Keywords
Citation
1. Acquistapace, F., Broglia, F., Shiota, M.: The finiteness property and Łojasiewicz inequality for global semianalytic sets. Adv. Geom. 5, 453–466 (2005)
2. Acquistapace, F., Broglia, F., Tognoli, A.: Sull’insieme di non-coerenza di un insieme analitico reale.Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 55, 42–45 (1973)
3. Andradas, C., Bröcker, L., Ruiz, J.M.: Minimal generation of basic open semianalytic sets. Invent.Math. 92(2), 409–430 (1988)
4. Andradas, C., Bröcker, L., Ruiz, J.M.: Constructible sets in real geometry. In: Ergeb. Math., vol. 33.Springer, Berlin (1996)
5. Andradas, C., Castilla, A.: Connected components of global semianalytic subsets of 2-dimensional analyticmanifolds. J. Reine Angew. Math. 475, 137–148 (1996)
6. Andreotti, A., Stoll, W.: Analytic and algebraic dependence of meromorphic functions. In: Lecture Notes in Mathematics, vol. 234. Springer, Berlin (1971)
7. Bierstone, E., Milman, P.D.: Semianalytic and subanalytic sets. Inst. Hautes Études Sci. Publ. Math.67, 5–42 (1988)
8. Bierstone, E., Milman, P.D.: Subanalytic geometry. In: Model Theory, Algebra, and Geometry, pp. 151–172. Mathematical Sciences Research Institute Publications, vol. 39. Cambridge University Press, Cambridge (2000)
9. Bruhat, F., Cartan, H.: Sur les composantes irréductibles d’un sous-ensemble analytique-réel. C. R. Acad. Sci. Paris 244, 1123–1126 (1957)
10. Cartan, H.: Variétés analytiques réelles et variétés analytiques complexes. Bull. Soc. Math. Fr. 85, 77–99 (1957)
11. Cartan, H.: Sur les fonctions de plusieurs variables complexes: les espaces analytiques. In: Proceedings of the International Congress of Mathematicians 1958, pp. 33–52. Cambridge University Press, New York (1960)
12. Denkowska, Z.: La continuité de la section d’un ensemble semi-analytique et compact. Ann. Polon. Math. 37(3), 231–242 (1980)
13. Fensch, W.: Reell-analytische Strukturen. Schr. Math. Inst. Univ. Münster 34, 56 pp. (1966)
14. Fernando, J.F.: On the irreducible components of globally defined semianalytic sets (2015). Preprint RAAG. arXiv:1503.00990
15. Gabrielov, A.: Projections of semi-analytic sets. Funct. Anal. Appl. 2(4), 282–291 (1968)
16. Galbiati, M.: Stratifications et ensemble de non-cohérence d’un espace analytique réel. Invent. Math. 34(2), 113–128 (1976)
17. Galbiati, M.: Sur l’image d’un morphisme analytique réel propre. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3(2), 311–319 (1976)
18. Guaraldo, F., Macrì, P., Tancredi, A.: Topics on real analytic spaces. In: Advanced Lectures in Mathematics.Friedr. Vieweg & Sohn, Braunschweig (1986)
19. Gunning, R., Rossi, H.: Analytic Functions of Several Complex Variables. Prentice Hall, Englewood Cliff (1965)
20. Hardt, R.M.: Homology and images of semianalytic sets. Bull. Am. Math. Soc. 80, 675–678 (1974)
21. Hardt, R.M.: Homology theory for real analytic and semianalytic sets. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2(1), 107–148 (1975)
22. Hironaka, H.: Introduction aux ensembles sous-nalytiques. In: Rédigé par André Hirschowitz et
Patrick Le Barz. Singularités à Cargèse (Rencontre Singularités en Géom. Anal., Inst. Études Sci., Cargèse, 1972), pp. 13–20. Asterisque, 7 et 8. Soc. Math. France, Paris (1973)
23. Hironaka, H.: Subanalytic sets. In: Number Theory, Algebraic Geometry and Commutative Algebra. In honor of Yasuo Akizuki, pp. 453–493. Kinokuniya, Tokyo (1973)
24. Hironaka, H.: Introduction to real-analytic sets and real-analytic maps. In: Quaderni dei Gruppi di Ricerca Matematica del Consiglio Nazionale delle Ricerche. Istituto Matematico “L. Tonelli” dell’Università di Pisa, Pisa (1973)
25. Hironaka, H.: Stratification and flatness. In: Real and Complex Singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), pp. 199-265. Sijthoff and Noordhoff, Alphen aan den Rijn (1977)
26. de Jong, T., Pfister, G.: Local analytic geometry. Basic theory and applications. In: Advanced Lectures in Mathematics. Friedr. Vieweg & Sohn, Braunschweig (2000)
27. Kurdyka, K.: Des applications du théorème de Puiseux dans la théorie des ensembles semi-analytiques dans R2. Univ. Iagel. Acta Math. 26, 105–113 (1987)
28. Łojasiewicz, S.: Ensembles semi-analytiques, Cours Faculté des Sciences d’Orsay, Mimeographié I.H.E.S., Bures-sur-Yvette, July (1965). http://perso.univ-mennes1.fr/michel.coste/Lojasiewicz
29. Łojasiewicz, S.: Triangulation of semi-analytic sets. Ann. Scuola Norm. Sup. Pisa 3(18), 449–474 (1964)
30. Matsumura, H.: Commutative algebra, 2nd edn. In: Mathematics Lecture Note Series, vol. 56. Benjamin/Cummings
Publishing Co., Inc., Reading (1980)
31. Narasimhan, R.: Introduction to the theory of analytic spaces. In: Lecture Notes in Mathematics, vol. 25. Springer, Berlin (1966)
32. Narasimhan, R.: Analysis on real and complex manifolds. In: Advanced Studies in Pure Mathematics, vol. 1. Masson & Cie, Éditeurs/North-Holland Publishing Co., Paris/Amsterdam (1968)
33. Narasimhan, R.: A note on Stein spaces and their normalisations. Ann. Scuola Norm. Sup. Pisa 3(16), 327–333 (1962)
34. Oka, K.: Sur les fonctions analytiques de plusieurs variables. VIII. Lemme fondamental. J. Math. Soc.Jpn. 3, 204–214 (1951)
35. Parusi ´nski, A.: Lipschitz properties of semi-analytic sets. Ann. Inst. Fourier (Grenoble) 38(4), 189–213 (1988)
36. Pawłucki, W.: Sur les points réguliers d’un ensemble semi-analytique. Bull. Pol. Acad. Sci. Math. 32(9–10), 549–553 (1984)
37. Quarez, R.: The Noetherian space of abstract locally Nash sets. Commun. Algebra 26(6), 1945–1966 (1998)
38. Ruiz, J.M.: On the real spectrum of a ring of global analytic functions. In: Algèbre, 84–95. Publ. Inst. Rech. Math. Rennes, 1986-4. Univ. Rennes I, Rennes (1986)
39. Ruiz, J.M.: On the connected components of a global semianalytic set. J. Reine Angew. Math. 392,137–144 (1988)
40. Ruiz, J.M.: On the topology of global semianalytic sets. In: Real Analytic and Algebraic Geometry (Trento, 1988), pp. 237–246. Lecture Notes in Mathematics, vol. 1420. Springer, Berlin (1990)
41. Shiota, M.: Geometry of subanalytic and semialgebraic sets. In: Progress in Mathematics, vol. 150. Birkhäuser Boston, Inc., Boston (1997)
42. Stasica, J.: Smooth points of a semialgebraic set. Ann. Polon. Math. 82(2), 149–153 (2003)
43. Tancredi, A., Tognoli, A.: On a decomposition of the points of noncoherence of a real analytic space.Riv. Mat. Univ. Parma (4) 6, 401–405 (1980)
44. Tognoli, A.: Proprietà globali degli spazi analitici reali. Ann. Mat. Pura Appl. 4(75), 143–218 (1967)45. Whitney, H., Bruhat, F.: Quelques propiétés fondamentales des ensembles analytiques réels. Comment.Math. Helv. 33, 132–160 (1959)