# On the metric dimension of converging sequences

Ladislav, Jr. Mišík; Tibor Žáčik

Commentationes Mathematicae Universitatis Carolinae (1993)

- Volume: 34, Issue: 2, page 367-373
- ISSN: 0010-2628

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topMišík, Ladislav, Jr., and Žáčik, Tibor. "On the metric dimension of converging sequences." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 367-373. <http://eudml.org/doc/247460>.

@article{Mišík1993,

abstract = {In the paper, some kind of independence between upper metric dimension and natural order of converging sequences is shown — for any sequence converging to zero there is a greater sequence with an arbitrary ($\leqslant 1$) upper dimension. On the other hand there is a relationship to summability of series — the set of elements of any positive summable series must have metric dimension less than or equal to $1/2$.},

author = {Mišík, Ladislav, Jr., Žáčik, Tibor},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {metric dimension; converging sequences; summability of series; metric dimension; converging sequences; summability of series},

language = {eng},

number = {2},

pages = {367-373},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On the metric dimension of converging sequences},

url = {http://eudml.org/doc/247460},

volume = {34},

year = {1993},

}

TY - JOUR

AU - Mišík, Ladislav, Jr.

AU - Žáčik, Tibor

TI - On the metric dimension of converging sequences

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1993

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 34

IS - 2

SP - 367

EP - 373

AB - In the paper, some kind of independence between upper metric dimension and natural order of converging sequences is shown — for any sequence converging to zero there is a greater sequence with an arbitrary ($\leqslant 1$) upper dimension. On the other hand there is a relationship to summability of series — the set of elements of any positive summable series must have metric dimension less than or equal to $1/2$.

LA - eng

KW - metric dimension; converging sequences; summability of series; metric dimension; converging sequences; summability of series

UR - http://eudml.org/doc/247460

ER -

## References

top- Kolmogorov A. N., Tihomirov V. M., $\epsilon $-entropy and $\epsilon $-capacity of sets in functional spaces (in Russian), Usp. Mat. Nauk 14 (1959), 3-86 Am. Math. Soc. Transl. 17 (1961), 277-364. (1961) MR0112032
- Mišík L., Žáčik T., On some properties of the metric dimension, Comment. Math. Univ. Carolinae 31 (1990), 781-791. (1990) MR1091376
- Pontryagin L.S., Snirelman L.G., Sur une propriété 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
- Vosburg A.C., On the relationship between Hausdorff dimension and metric dimension, Pacific J. Math. 23 (1967), 183-187. (1967) Zbl0153.24701MR0217776
- Yomdin Y., The geometry of critical and near-critical values of differentiable mappings, Math. Ann. 264 (1983), 495-515. (1983) Zbl0507.57019MR0716263
- Žáčik T., On some approximation properties of the metric dimension, Math. Slovaca 42 (1992), 331-338. (1992) MR1182963

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