On some properties of the metric dimension

Ladislav Mišík; Tibor Žáčik

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 4, page 781-791
  • ISSN: 0010-2628

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Mišík, Ladislav, and Žáčik, Tibor. "On some properties of the metric dimension." Commentationes Mathematicae Universitatis Carolinae 031.4 (1990): 781-791. <http://eudml.org/doc/17900>.

@article{Mišík1990,
author = {Mišík, Ladislav, Žáčik, Tibor},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {entropy dimension; limit capacity; covering functions; metric dimensions},
language = {eng},
number = {4},
pages = {781-791},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On some properties of the metric dimension},
url = {http://eudml.org/doc/17900},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Mišík, Ladislav
AU - Žáčik, Tibor
TI - On some properties of the metric dimension
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 4
SP - 781
EP - 791
LA - eng
KW - entropy dimension; limit capacity; covering functions; metric dimensions
UR - http://eudml.org/doc/17900
ER -

References

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  1. Bakhtin V. I., Properties of the entropy and Hausdorff dimension (in Russian), Vestnik Moskov. Univ. Ser. 1 Mat. Meh. 15 (1982), 25-29. (1982) MR0679473
  2. Besicovitch A. S., Taylor S. J., On the complementary intervals of a linear closed sets of zero Lebesgue measure, L. London Math. Soc. 29 (1954), 449-459. (1954) MR0064849
  3. Cajar H., Sandan K., Perfekte Mengen mit unterschiedlicher Hausdorff und unterer metrischer Dimension, Arch. Math. 45 (1985), 21-33. (1985) MR0799446
  4. Hawkes J., Hausdorff measure, entropy, and the independence of small sets, Proc. London Math. Soc. (3) 28 (1974), 700-724. (1974) Zbl0315.28001MR0352412
  5. Kolmogorov A. N., Tihomirov V. M., e-entropy and e-capacity of sets in functional spaces (in Russian), Usp. Mat. Nauk 14 (1959), 3-86; Am. Math. Soc. Transl. IT (1961), 277-364. (1959) MR0112032
  6. Maňé R., On the dimension of the compact invariant sets of certain nonlinear maps, "Dynamical Systems and Turbulence", Warwick 1980 (Coventry 1979/1980), Lecture Notes in Math. 898, Springer, Berlin - New York 1981, 230-242. (1980) MR0654892
  7. Prosser R. T., Note on metric dimension, Proc. Amer. Math. Soc. 25 (1970), 763-765. (1970) Zbl0197.19303MR0259873
  8. Pontryagin L. S., Snirelman L. G., Sur une proprieie metrique de la dimension, Annals of Math. 33 (1932), 156-162. Appendix to the Russian translation of "Dimension Theory" by W. Hurewitcz and H. Wallman, Izdat. Inostr. Lit. Moscow, 1948. (1932) MR1503042
  9. Palis J., Takens F., Hyperbolicity and the creation of homoclinic orbits, Annals of Mathematics 125 (1987), 337-374. (1987) Zbl0641.58029MR0881272
  10. Vosburg A. C., On the relationship between Hausdorff dimension and metric dimension, Pacific J. Math. 23 (1967), 183-187. (1967) Zbl0153.24701MR0217776
  11. Yomdin Y., The geometry of critical and near-critical values of differentiable mappings, Math. Ann. 264 (1983), 495-515. (1983) Zbl0507.57019MR0716263

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