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A note on a separation problem

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dc.contributor.authorRuiz Sancho, Jesús María
dc.date.accessioned2023-06-21T02:04:08Z
dc.date.available2023-06-21T02:04:08Z
dc.date.issued1984
dc.description.abstractThe author proves the following theorem: Let A0 be a closed 1-dimensional semianalytic germ at the origin 0∈Rn. Let Z be a semianalytic set in Rn whose germ Z0 at 0 is closed and A0∩Z0={0}. Then there exists a polynomial h∈R[x1,⋯,xn] such that h∣Z∖{0}>0 and h∣A0∖{0}<0. The proof is by induction on the number of blowing-ups needed to "solve" the set A0. Some implications are then given, in particular a similar result for semialgebraic sets in Rn and polynomials.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/20293
dc.identifier.citationG. W. BRUMFIEL, Some open problems, in Ordered fields and real algebraic geometry. Contemporary Math. 8, Amer. Math. Soc. (1982). S. LOJASIEWICZ, Ensembles semi-analytiques. Lecture Notes 1965 at I.H.E.S., Bures-sur-Yvette; reproduit n. 466.765, Ecole Polythecnique, Paris. T. MOSTOWSKI, Some properties of the ring of Nash functions. Ann. Scuola Norm. Sup. Pisa, III, 243-266 (1976). J. J. RISLER, Sur le théoreme des fonctions composées différentiables. Ann. Institut Fourier, 32 (2), 229-260 (1982). J. M. RUIZ, Central orderings in fields of real meromorphic function germs. Manuscripta Math. 46, 1-3, 193-214 (1984).
dc.identifier.doi10.1007/BF01193850
dc.identifier.issn0003-889X
dc.identifier.officialurlhttp://link.springer.com/content/pdf/10.1007%2FBF01193850
dc.identifier.relatedurlhttp://www.springer.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/64767
dc.issue.number5
dc.journal.titleArchiv der Mathematik
dc.language.isoeng
dc.page.final426
dc.page.initial422
dc.publisherBirkhäuser Verlag
dc.rights.accessRightsrestricted access
dc.subject.cdu512.7
dc.subject.cdu515.171.5
dc.subject.keywordSeparation problem
dc.subject.keywordsemianalytic germ
dc.subject.keywordanalytic function germ
dc.subject.keywordsemialgebraic sets
dc.subject.ucmGeometria algebraica
dc.subject.unesco1201.01 Geometría Algebraica
dc.titleA note on a separation problem
dc.typejournal article
dc.volume.number43
dspace.entity.typePublication
relation.isAuthorOfPublicationf12f8d97-65c7-46aa-ad47-2b7099b37aa4
relation.isAuthorOfPublication.latestForDiscoveryf12f8d97-65c7-46aa-ad47-2b7099b37aa4
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