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Semialgebraic topology over a real closed field I: Paths and components in the set of rational points of an algebraic variety

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References

  1. Artin, E.: Über die Zerlegung definiter Funktionen in Quadrate, Abh. Math. Sem. Univ. Hamburg5, 100–115 (1927)

    Google Scholar 

  2. Brumfiel, G.W.: Partially ordered rings and semi-algebraic geometry. London Math. Soc. Lecture Note Series 37, Cambridge U.P. 1979

  3. Cohen, P.J.: Decesion procedures for real andp-adic fields. Comm. pure appl. math.22, 131–151 (1969)

    Google Scholar 

  4. Colliot-Thélène, J.L., Sansuc, J.J.: Fibrés quadratiques et composantes connexes réelles. Math. Ann.224, 105–134 (1979)

    Google Scholar 

  5. Coste-Roy, M.F., Coste, M.: Topologies for real algebraic geometry, in: A. Kock ed., Topos theoretic methods in geometry. Various Publications Series no. 30, Aarhus Universitet (1979)

  6. Dietel, G.: Thesis on the Witt rings of curves over real closed fields, Regensburg, in preparation

  7. Fehlner, J.: Analysis der Morphismen von Kurven über reell abgeschlossenen Körpern, Staatsexamensarbeit Regensburg 1978

  8. Geyer, W.D.: Reelle algebraische Funktionen mit vorgegebenen Null-und Polstellen. Manuscr. math.22, 87–103 (1977)

    Google Scholar 

  9. Grothendieck, A., Illusie, L.: Théorie des intersections et théorème de Riemann-Roch. Seminaire de Géometrie algébrique du Bois Marie 1966/67. Lecture Notes Math.225. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  10. Knebusch, M.: On algebraic curves over real closed fields I, II. Math. Z.150, 49–70;151, 189–205 (1976)

    Google Scholar 

  11. Knebusch, M.: Real closures of commutative rings I, II. M. reine angew. Math.274/275, 61–89 (1975);286/287, 278–313 (1976)

    Google Scholar 

  12. Knebusch, M.: Symmetric bilinear forms over algebraic varieties. In: Conference on quadratic forms (Kingston 1976), pp. 103–283. Queen's papers in Pure Appl. Math.46 (1977)

  13. Knebusch, M.: Real closures of algebraic varieties, ibid. In: Conference on quadratic forms (Kingston 1976), pp. 548–568 Queen's papers in Pure Appl. Math.46 (1977)

  14. Knebusch, M.: Spezialization of quadratic and symmetric bilinear forms, and a norm theorem. Acta arithm.24, 279–299 (1973)

    Google Scholar 

  15. Knebusch, M.: On the uniqueness of real closures and the existence of real places. Comment. math. Helv.47, 260–269 (1972)

    Google Scholar 

  16. Lang, S.: The theory of real places. Ann. Math.57, 378–391 (1953)

    Google Scholar 

  17. Witt, E.: Zerlegung reeller algebraischer Funktionen in Quadrate, Schiefkörper über reellem Funktionenkörper, J. reine angew. Math.171, 4–11 (1934)

    Google Scholar 

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  1. Fachbereich Mathematik der Universität, Universitätsstr. 31, D-8400, Regensburg, Federal Republic of Germany

    Hans Delfs & Manfred Knebusch

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  1. Hans Delfs
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  2. Manfred Knebusch
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Delfs, H., Knebusch, M. Semialgebraic topology over a real closed field I: Paths and components in the set of rational points of an algebraic variety. Math Z 177, 107–129 (1981). https://doi.org/10.1007/BF01214342

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