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On a shadowing lemma in metric spaces

Tibor Žáčik — 1992

Mathematica Bohemica

In the present paper conditions are studied, under which a pseudo-orbit of a continuous map f : M M , where M is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map f .

On the metric dimension of converging sequences

Ladislav, Jr. MišíkTibor Žáčik — 1993

Commentationes Mathematicae Universitatis Carolinae

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 ( 1 ) 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 1 / 2 .

A formula for calculation of metric dimension of converging sequences

Ladislav, Jr. MišíkTibor Žáčik — 1999

Commentationes Mathematicae Universitatis Carolinae

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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