Problems of homeomorphism arising in the theory of grid generation

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Abstract

Some general criteria of being a homeomorphism for continuous maps of topological spaces and topological manifolds are proved in this paper, as well as criteria of being a diffeomorphism for smooth maps of smooth manifolds.

References

  1. 1.
    O. V. Ushakova, Proc. Steklov Inst. Math. Suppl. 1, S78 (2004).MathSciNetGoogle Scholar
  2. 2.
    O. V. Ushakova, in Advances in Grid Generation, Ed. by O. V. Ushakova (Nova Science, New York, 2007), pp. 241–278.Google Scholar
  3. 3.
    N. A. Bobylev, S. A. Ivanenko, and I. G. Ismailov, Mat. Zametki 60(4), 593 (1996).MathSciNetGoogle Scholar
  4. 4.
    N. A. Bobylev, S. A. Ivanenko, and A. V. Kazunin, Zh. Vychisl. Mat. Mat. Fiz. 43(6), 808 (2003).MATHMathSciNetGoogle Scholar
  5. 5.
    M. F. Prokhorova, in Problems of Theoretical and Applied Mathematics (UrO RAN, Yekaterinburg, 2007), pp. 65–69 [in Russian].Google Scholar
  6. 6.
    A. Dold, Lectures on Algebraic Topology (Springer-Verlag, Berlin, 1972; Mir, Moscow, 1976).MATHGoogle Scholar
  7. 7.
    V. A. Rokhlin and D. B. Fuks, Beginner’s Course in Topology: Geometric Chapters (Nauka, Moscow, 1977; Springer-Verlag, Berlin, 1984).Google Scholar
  8. 8.
    D. Novikov and A. Khovanskii, Mosc. Math. J. 6(1), 135 (2006).MATHMathSciNetGoogle Scholar
  9. 9.
    M. Brown, Ann. of Math. 75(2), 331 (1962).CrossRefMathSciNetGoogle Scholar
  10. 10.
    P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory. Introduction to the Theory of Topological Spaces and to General Dimension Theory (Nauka, Moscow, 1973) [in Russian].Google Scholar
  11. 11.
    E. Spanier, Algebraic topology (McGraw-Hill, New York, 1966; Mir, Moscow, 1971).MATHGoogle Scholar
  12. 12.
    J. Mankres, Elementary Differential Topology (Princeton Univ., Princeton, NJ, 1963).Google Scholar
  13. 13.
    G. H. Meisters and C. Olech, Duke Math. J. 30(1), 63 (1963).MATHCrossRefMathSciNetGoogle Scholar
  14. 14.

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsUral Branch of the Russian Academy of SciencesYekaterinburgRussia

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