Geodesic
On the metric dimension of converging sequences
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 2, pp. 367-373

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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 ($\leqslant 1$) 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 $1/2$.
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 ($\leqslant 1$) 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 $1/2$.
Classification : 40A05, 40J05, 54E35, 54E45, 54F45, 54F50
Keywords: metric dimension; converging sequences; summability of series 
Mišík, Ladislav, Jr.; Žáčik, Tibor. On the metric dimension of converging sequences. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 2, pp. 367-373. http://geodesic.mathdoc.fr/item/CMUC_1993_34_2_a19/
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     title = {On the metric dimension of converging sequences},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {367--373},
     year = {1993},
     volume = {34},
     number = {2},
     mrnumber = {1241746},
     zbl = {0845.54026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993_34_2_a19/}
}
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