Publication: A note on a separation problem
dc.contributor.author | Ruiz Sancho, Jesús María | |
dc.date.accessioned | 2023-06-21T02:04:08Z | |
dc.date.available | 2023-06-21T02:04:08Z | |
dc.date.issued | 1984 | |
dc.description.abstract | The 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.department | Depto. de Álgebra, Geometría y Topología | |
dc.description.faculty | Fac. de Ciencias Matemáticas | |
dc.description.refereed | TRUE | |
dc.description.status | pub | |
dc.eprint.id | https://eprints.ucm.es/id/eprint/20293 | |
dc.identifier.citation | G. 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.doi | 10.1007/BF01193850 | |
dc.identifier.issn | 0003-889X | |
dc.identifier.officialurl | http://link.springer.com/content/pdf/10.1007%2FBF01193850 | |
dc.identifier.relatedurl | http://www.springer.com | |
dc.identifier.uri | https://hdl.handle.net/20.500.14352/64767 | |
dc.issue.number | 5 | |
dc.journal.title | Archiv der Mathematik | |
dc.language.iso | eng | |
dc.page.final | 426 | |
dc.page.initial | 422 | |
dc.publisher | Birkhäuser Verlag | |
dc.rights.accessRights | restricted access | |
dc.subject.cdu | 512.7 | |
dc.subject.cdu | 515.171.5 | |
dc.subject.keyword | Separation problem | |
dc.subject.keyword | semianalytic germ | |
dc.subject.keyword | analytic function germ | |
dc.subject.keyword | semialgebraic sets | |
dc.subject.ucm | Geometria algebraica | |
dc.subject.unesco | 1201.01 Geometría Algebraica | |
dc.title | A note on a separation problem | |
dc.type | journal article | |
dc.volume.number | 43 | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 | |
relation.isAuthorOfPublication.latestForDiscovery | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 |
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