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On Typical Compact Submanifolds of the Euclidean Space

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Ukrainian Mathematical Journal Aims and scope

It is shown that typical compact submanifolds of R n are nowhere differentiable with integer box dimensions.

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References

  1. S. Banach, “Uberdie Baire’sche kategorie gewisser funktionenmengen,” Stud. Math., 3, 147–179 (1931).

    Google Scholar 

  2. A. S. Besicovitch and H. D. Ursell, “On dimensional numbers of some curves,” J. London Math. Soc., 12, 18–25 (1937).

    Google Scholar 

  3. W. L. Bloch, “Fractal boundaries are not typical,” Topol. Appl., 145, 553–539 (2007).

    MathSciNet  Google Scholar 

  4. K. Falconer, Fractal Geometry: Mathematical Foundations, Wiley, New York (1990).

    MATH  Google Scholar 

  5. P. Gruber, “Dimension and structure of typical compact sets, continua and curves,” Mh. Math., 108, 149–164 (1989).

    Article  MATH  Google Scholar 

  6. R. Mirzaie, “On images of continuous functions from a compact manifold into Euclidean space,” Bull. Iran. Math. Soc., 37, 93–100 (2011).

    MATH  MathSciNet  Google Scholar 

  7. J. R. Munkres, “Topology. A first course,” Appl. Century Grotfs (2000).

  8. A. Ostaszewski, “Families of compact sets and their universals,” Mathematica, 21, 116–127 (1974).

    MATH  MathSciNet  Google Scholar 

  9. W. Rudin, “Principles of mathematical analysis,” MGH (1976).

  10. J. A. Wieacker, “The convex hull of a typical compact set,” Math. Ann., 282, 637–644 (1998).

    Article  MathSciNet  Google Scholar 

  11. T. Zamfirescu, “How many sets are porous?,” Proc. Amer. Math. Soc., 100, 383–387 (1987).

    Article  MATH  MathSciNet  Google Scholar 

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 1009–1014, July, 2013.

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Mirzaie, R. On Typical Compact Submanifolds of the Euclidean Space. Ukr Math J 65, 1126–1133 (2013). https://doi.org/10.1007/s11253-013-0847-x

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  • DOI: https://doi.org/10.1007/s11253-013-0847-x

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