1999•Unpublished venueRequires access

A formula for calculation of metric dimension of converging sequences

Ladislav Miÿs ́ õk

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, respec- tively) 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, Dimension function, Inductive dimension, Mathematics, Effective dimension, Dimension (graph theory)