A simplified formula for calculation of metric dimension of converging sequences

Tibor Žáčik; Ladislav Mišík

Mathematica Slovaca (2005)

  • Volume: 55, Issue: 3, page 363-372
  • ISSN: 0139-9918

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Žáčik, Tibor, and Mišík, Ladislav. "A simplified formula for calculation of metric dimension of converging sequences." Mathematica Slovaca 55.3 (2005): 363-372. <http://eudml.org/doc/32025>.

@article{Žáčik2005,
author = {Žáčik, Tibor, Mišík, Ladislav},
journal = {Mathematica Slovaca},
keywords = {metric dimension; box-counting dimension; limit capacity; Kolmogorov dimension; Minkowski dimension; Bouligand dimension; entropy dimension; Hausdorff dimension; converging sequences; convex sequence; differentiable function},
language = {eng},
number = {3},
pages = {363-372},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A simplified formula for calculation of metric dimension of converging sequences},
url = {http://eudml.org/doc/32025},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Žáčik, Tibor
AU - Mišík, Ladislav
TI - A simplified formula for calculation of metric dimension of converging sequences
JO - Mathematica Slovaca
PY - 2005
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 55
IS - 3
SP - 363
EP - 372
LA - eng
KW - metric dimension; box-counting dimension; limit capacity; Kolmogorov dimension; Minkowski dimension; Bouligand dimension; entropy dimension; Hausdorff dimension; converging sequences; convex sequence; differentiable function
UR - http://eudml.org/doc/32025
ER -

References

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  1. BESICOVITCH A. S.-TAYLOR S. J., On the complementary intervals of a linear closed sets of zero Lebesgue measure, J. London Math. Soc. 29 (1954), 449-459. (1954) MR0064849
  2. HAWKES J., Hausdorff measure, entropy and the independents of small sets, Proc. London Math. Soc. (3) 28 (1974), 700-724. (1974) MR0352412
  3. KOCAK S.-AZCAN H., Fractal dimensions of some sequences of real numbers, Doga Mat. 17 (1993), 298-304. (1993) Zbl0857.40002MR1255026
  4. KOLMOGOROV A. N.-TIKHOMIROV V. M., ϵ -entropy and ϵ -capacity of sets in functional spaces, Uspekhi Mat. Nauk 14 (1959), 3 86 (Russian); In: Amer. Math. Soc. Transl. Ser. 2 Vol. 17, Amer. Math. Soc, Providence, RI, 1961, pp. 277-364. (1959) MR0112032
  5. MIŠÍK L.-ŽÁČIK T., On some properties of the metric dimension, Comment. Math. Univ. Carolin. 31 (1990), 781-791. (1990) Zbl0717.54017MR1091376
  6. MIŠÍK L.-ŽÁČIK T., A formula for calculation of metric dimension of converging sequences, Comment. Math. Univ. Carolin. 40 (1999), 393-401. (1999) Zbl0976.54035MR1732660
  7. PONTRYAGIN L. S.-SNIRELMAN L. G., Sur une propriete metrique de la dimension, Ann. of Math. (2) 33 (1932), 156-162 (Appendix to the Russian translation of Dimension Theory by W. Hurewitcz and H. Wallman, Izdat. Inostr. Lit., Moscow, 1948). (1932) Zbl0003.33101MR1503042

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