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On open and closed morphisms between semialgebraic sets


Authors: José F. Fernando and J. M. Gamboa
Journal: Proc. Amer. Math. Soc. 140 (2012), 1207-1219
MSC (2010): Primary 14P10, 54C30; Secondary 12D15, 13E99
DOI: https://doi.org/10.1090/S0002-9939-2011-10989-4
Published electronically: August 2, 2011
MathSciNet review: 2869106
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Abstract | References | Similar Articles | Additional Information

Abstract: 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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References
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Additional Information

José F. Fernando
Affiliation: Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: josefer@mat.ucm.es

J. M. Gamboa
Affiliation: Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: jmgamboa@mat.ucm.es

Keywords: Semialgebraic function, semialgebraic set, Zariski spectrum, maximal spectrum, open and closed maps, proper map, Bezoutian, quotient map.
Received by editor(s): July 26, 2010
Received by editor(s) in revised form: January 3, 2011
Published electronically: August 2, 2011
Additional Notes: The authors were supported by the Spanish GAAR MTM2008-00272, Proyecto Santander Complutense PR34/07-15813 and GAAR Grupos UCM 910444
Communicated by: Lev Borisov
Article copyright: © Copyright 2011 American Mathematical Society