A Cantor set in the plane and its monotone subsets
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  • 作者:A. Nekvinda
  • 关键词:monotone metric space ; Cantor set ; Hausdorff measure ; Hausdorff dimension ; 54F05 ; 28A78 ; 28A80
  • 刊名:Acta Mathematica Hungarica
  • 出版年:2016
  • 出版时间:February 2016
  • 年:2016
  • 卷:148
  • 期:1
  • 页码:43-55
  • 全文大小:643 KB
  • 参考文献:1.K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley (Chichester, 1990).
    2.Hrušák M., Nekvinda A., Vlasák V., Zindulka O.: Properties of functions with monotone graphs. Acta Math. Hungar 142, 1–30 (2013)
    3.Hrušák M., Zindulka O.: Cardinal invariants of monotone and porous sets. J. Symbolic Logic 77, 159–173 (2012)MathSciNet CrossRef MATH
    4.Keleti T., Máthé A., Zindulka O.: Hausdorff dimension of metric spaces and Lipschitz maps onto cubes. Int. Math. Res. Not. 2, 289–302 (2014)
    5.Mendel M., Naor A.: Ultrametric subsets with large Hausdorff dimension. Invent. Math. 192, 1–54 (2013)MathSciNet CrossRef MATH
    6.Nekvinda A., Pokorný D., Vlasák V.: Some results on monotone metric spaces. J. Math. Anal. Appl. 413, 999–1016 (2014)MathSciNet CrossRef MATH
    7.Nekvinda A., Zindulka O.: A Cantor set in the plane that is not σ-monotone. Fund. Math. 213, 221–232 (2011)MathSciNet CrossRef MATH
    8.Nekvinda A., Zindulka O.: Monotone metric spaces. Order 29, 545–558 (2012)MathSciNet CrossRef MATH
    9.Schief A.: Self-similar sets in complete metric spaces. Proc. Amer. Math. Soc. 124, 481–490 (1996)MathSciNet CrossRef MATH
    10.Zindulka O.: Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps. Fund. Math. 218, 95–119 (2012)MathSciNet CrossRef MATH
  • 作者单位:A. Nekvinda (1)

    1. Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 160 00, Prague 6, Czech Republic
  • 刊物类别:Mathematics and Statistics
  • 刊物主题:Mathematics
    Sciences
    Mathematics
  • 出版者:Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
  • ISSN:1588-2632
文摘
Given c >  0 a planar Cantor set X with a dim H (X) < 2 is constructed such that each c-monotone subspace of X has a smaller Hausdorff dimension than X. Key words and phrases monotone metric space Cantor set Hausdorff measure Hausdorff dimension

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