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On the metric dimension of converging sequences

Ladislav, Jr. Mišík, Tibor 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 .

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