Título:
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On the semialgebraic Stone-?ech compactification of a semialgebraic set
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Autores:
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Fernando Galván, José Francisco ;
Gamboa, J. M.
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Tipo de documento:
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texto impreso
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Editorial:
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American Mathematical Society, 2012
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/restrictedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Geometria algebraica
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Tipo = Artículo
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Resumen:
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In the same vein as the classical Stone–?Cech compactification, we prove in this work that the maximal spectra of the rings of semialgebraic and bounded semialgebraic functions on a semialgebraic set M ? Rn, which are homeomorphic topological spaces, provide the smallest Hausdorff compactification of M such that each bounded R-valued semialgebraic function on M extends continuously to it. Such compactification ??sM, which can be characterized as the smallest compactification that dominates all semialgebraic compactifications of M, is called the semialgebraic Stone– ? Cech compactification of M, although it is very rarely a semialgebraic set. We are also interested in determining the main topological properties of the remainder ?M = ??sM \M and we prove that it has finitely many connected components and that this number equals the number of connected components of the remainder of a suitable semialgebraic compactification of M. Moreover, ?M is locally connected and its local compactness can be characterized just in terms of the topology of M.
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En línea:
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https://eprints.ucm.es/id/eprint/16315/1/Gamboa_50.pdf
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