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Jacobian and the Darboux Property

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Ukrainian Mathematical Journal Aims and scope

We present a simple proof of the Darboux property for the Jacobian of a differentiable mapping.

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References

  1. P. S. Aleksandrov, Combinatorial Topology [in Russian], GITTL, Moscow (1947), pp. 568–579.

  2. A.V. Chernavskii, “Finite-to-one open mappings of manifolds,” Mat. Sb., 65, 357–369 (1964).

    MathSciNet  Google Scholar 

  3. G. Väisälä, “Discrete open mappings on manifolds,” Ann. Acad. Sci. Fenn., I. Math., 392, 3–10 (1966).

    MathSciNet  MATH  Google Scholar 

  4. K. Steffen, “Über den Zwischenwertsatz von Darboux und den Umkehrsatz für differenzierbare Functionen mehrerer Veränderlicher,” Elen. Math., 37, No. 5, 121–131 (1982).

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  5. A. M. Rodnyanskii, “On the differentiable mappings of domains,” Dokl. Akad. Nauk SSSR, 72, 15–17 (1950).

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 10, pp. 1439–1440, October, 2015.

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Trokhimchuk, Y.Y. Jacobian and the Darboux Property. Ukr Math J 67, 1618–1620 (2016). https://doi.org/10.1007/s11253-016-1177-6

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  • DOI: https://doi.org/10.1007/s11253-016-1177-6

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