Abstract: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 $1/2$.
Keywords: metric dimension, converging sequences, summability of series
AMS Subject Classification: 54F50, 40A05