Geodesic
A formula for calculation of metric dimension of converging sequences
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 393-401 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 26A51, 40A05, 54F50
Keywords: metric dimension; limit capacity; entropy dimension; box-counting dimension; Hausdorff dimension; Kolmogorov dimension; Minkowski dimension; Bouligand dimension; converging sequences; convex sequences; differentiable function 
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     title = {A formula for calculation of metric dimension of converging sequences},
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Mišík, Ladislav, Jr.; Žáčik, Tibor. A formula for calculation of metric dimension of converging sequences. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 393-401. http://geodesic.mathdoc.fr/item/CMUC_1999_40_2_a20/