On a shadowing lemma in metric spaces
In the present paper conditions are studied, under which a pseudo-orbit of a continuous map , where is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map .
On some approximation properties of the metric dimension
On some properties of the metric dimension
A simplified formula for calculation of metric dimension of converging sequences
On the metric dimension of converging sequences
In the paper, some kind of independence between upper metric dimension and natural order of converging sequences is shown — for any sequence converging to zero there is a greater sequence with an arbitrary () upper dimension. On the other hand there is a relationship to summability of series — the set of elements of any positive summable series must have metric dimension less than or equal to .
A formula for calculation of metric dimension of converging sequences
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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