Converging sequences in metric space have Hausdorff dimension zero, but their metric dimension (limit capacity, entropy dimension, box-counting dimension, Hausdorff dimension, Kolmogorov dimension, Minkowski dimension, Bouligand dimension, respectively) can be positive. Dimensions of such sequences are calculated using a different approach for each type. In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived.
@article{119095,
author = {Ladislav, Jr. Mi\v s\'\i k and Tibor \v Z\'a\v cik},
title = {A formula for calculation of metric dimension of converging sequences},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {40},
year = {1999},
pages = {393-401},
zbl = {0976.54035},
mrnumber = {1732660},
language = {en},
url = {http://dml.mathdoc.fr/item/119095}
}
Mišík, Ladislav, Jr.; Žáčik, Tibor. A formula for calculation of metric dimension of converging sequences. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 393-401. http://gdmltest.u-ga.fr/item/119095/
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