1999•Commentationes Mathematicae Universitatis CarolinaeRequires access

A formula for calculation of metric dimension of converging sequences

Jr. Mišík Ladislav, Tibor Žáčik

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. In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived.

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Available abstract

Key concepts: Minkowski–Bouligand dimension, Packing dimension, Hausdorff dimension, Inductive dimension, Dimension function, Mathematics, Effective dimension, Dimension (graph theory)