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 $1/2$.
@article{118590,
author = {Ladislav, Jr. Mi\v s\'\i k and Tibor \v Z\'a\v cik},
title = {On the metric dimension of converging sequences},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {34},
year = {1993},
pages = {367-373},
zbl = {0845.54026},
mrnumber = {1241746},
language = {en},
url = {http://dml.mathdoc.fr/item/118590}
}
Mišík, Ladislav, Jr.; Žáčik, Tibor. On the metric dimension of converging sequences. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 367-373. http://gdmltest.u-ga.fr/item/118590/
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