On some approximation properties of the metric dimension

Tibor Žáčik

Mathematica Slovaca (1992)

  • Volume: 42, Issue: 3, page 331-338
  • ISSN: 0232-0525

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Žáčik, Tibor. "On some approximation properties of the metric dimension." Mathematica Slovaca 42.3 (1992): 331-338. <http://eudml.org/doc/31792>.

@article{Žáčik1992,
author = {Žáčik, Tibor},
journal = {Mathematica Slovaca},
keywords = {lower and upper metric dimension; compact subset; Hausdorff metric},
language = {eng},
number = {3},
pages = {331-338},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On some approximation properties of the metric dimension},
url = {http://eudml.org/doc/31792},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Žáčik, Tibor
TI - On some approximation properties of the metric dimension
JO - Mathematica Slovaca
PY - 1992
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 42
IS - 3
SP - 331
EP - 338
LA - eng
KW - lower and upper metric dimension; compact subset; Hausdorff metric
UR - http://eudml.org/doc/31792
ER -

References

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  1. BAKHTIN V. I., Properties of the entropy and Hausdorff dimension, (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh. 15 (1982), 25-29. (1982) MR0679473
  2. CAJAR H., SANDAN K., Perfekte Mengen mit unterschiedlicher Hausdorff und unterer metrischer Dimension, Arch. Math. 45 (1985), 21-33. (1985) MR0799446
  3. HAWKES J., Hausdorff measure, entropy, and the independence of small sets, Proc. London Math. Soc. (3) 28 (1974), 700-724. (1974) Zbl0315.28001MR0352412
  4. KOLMOGOROV A. N., TIHOMIROV V. M., e-entropy and e-capacity of sets in functional spaces, (Russian), Usp. Mat. Nauk 14 (1959), 3-86; Amer. Math. Soc. Transl. Ser. 2 17 (1961), 277-364. (1959) MR0112032
  5. 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, pp. 230-242. (1980) MR0654892
  6. MIŠÍK L., ŽÁČIK T., On some properties of the metric dimension, Comment. Math. Univ. Carolin. 31,4 (1990), 781-791. (1990) Zbl0717.54017MR1091376
  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 propriété métrique de la dimension, Ann. 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 homo clinic orbits, Ann. of Math. 125 (1987), 337-374. (1987) MR0881272
  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 differentiate mappings, Math. Ann. 264 (1983), 495-515. (1983) MR0716263

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