## Ladislav Mi{\v s}{\'\i }k Jr., Tibor {\v Z}{\'a}{\v c}ik

*A formula for calculation of metric dimension of converging sequences *

Comment.Math.Univ.Carolinae 40,2 (1999) 393-401. **Abstract:**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. \par In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived.

**Keywords:** metric dimension, limit capacity, entropy dimension, box-counting dimension, Hausdorff dimension, Kolmogorov dimension, Minkowski dimension, Bouligand dimension, converging sequences, convex sequences, differentiable function

**AMS Subject Classification:** 54F50, 40A05

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