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On Open And Closed Morphisms Between Semialgebraic Sets

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2012-04
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American Mathematical Society
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In this work we study how open and closed semialgebraic maps between two semialgebraic sets extend, via the corresponding spectral maps,to the Zariski and maximal spectra of their respective rings of semialgebraic and bounded semialgebraic functions.
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M.F. Atiyah, I.G. Macdonald: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ontario: 1969. MR0242802 (39:4129) J. Bochnak, M. Coste, M.-F. Roy: Real algebraic geometry. Ergeb. Math. 36, Springer- Verlag, Berlin: 1998. MR1659509 (2000a:14067) G.W. Brumfiel: Quotient spaces for semialgebraic equivalence relations. Math. Z. 195 (1987), no. 1, 69–78. MR888127 (88i:14015) J.F. Fernando: On chains of prime ideals in rings of semialgebraic functions. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/chains.pdf J.F. Fernando: On distinguished points of the remainder of the semialgebraic Stone–ˇCech compactification of a semialgebraic set. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/remainder.pdf J.F. Fernando, J.M. Gamboa: On the Krull dimension of rings of semialgebraic functions. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/dim.pdf J.F. Fernando, J.M. Gamboa: On the spectra of rings of semialgebraic functions. Collectanea Mathematica, to appear. http://www.mat.ucm.es/∼josefer/pdfs/ preprint/spectra.pdf J.F. Fernando, J.M. Gamboa: On Banach-Stone type theorems for semialgebraic sets. Preprint RAAG (2010). http://www.mat.ucm.es/∼josefer/pdfs/preprint/homeo.pdf J.F. Fernando, J.M. Gamboa: On the semialgebraic Stone–ˇCech compactification of a semialgebraic set. Trans. Amer. Math. Soc. (to appear). http://www.mat.ucm.es/ ∼josefer/pdfs/preprint/mspectra.pdf G. De Marco, A. Orsatti: Commutative rings in which every prime ideal is contained in a unique maximal ideal. Proc. Amer. Math. Soc. 30 (1971), no. 3, 459-466. MR0282962 (44:196) M.-A. Mulero: Algebraic properties of rings of continuous functions. Fund. Math. 149 (1996), no. 1, 55–66. MR1372357 (97c:16038) OPEN AND CLOSED MORPHISMS BETWEEN SEMIALGEBRAIC SETS 1219 V.I. Ponomarev: Open mappings of normal spaces. Dokl. Akad. Nauk SSSR 126 (1959), 716–718. MR0107855 (21:6577) C. Procesi, G. Schwarz: Inequalities defining orbit spaces. Invent. Math. 81 (1985), no. 3, 539–554. MR807071 (87h:20078) Departamento de ´Algebra, Facultad de Ciencias Matem´aticas, Universidad Complutense de Madrid, 28040 Madrid, Spain E-mail address: josefer@mat.ucm.es Departamento de ´Algebra, Facultad de Ciencias Matem´aticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
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