Metric dimension of complete metric spaces

Metric dimension of complete metric spaces
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Proc. Amer. Math. Soc. 24 (1970), 754-759

DOI: https://doi.org/10.1090/S0002-9939-1970-0257992-4

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References

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K. Nagami and J. H. Roberts, Metric-dependent dimension functions, Proc. Amer. Math. Soc. 16 (1965), 601–604. MR 195059, DOI 10.1090/S0002-9939-1965-0195059-2
Keiô Nagami and J. H. Roberts, A study of metric-dependent dimension functions, Trans. Amer. Math. Soc. 129 (1967), 414–435. MR 215289, DOI 10.1090/S0002-9947-1967-0215289-7

Dimension function

and covering dimension

K. Sitnikov, Example of a two-dimensional set in three-dimensional Euclidean space allowing arbitrarily small deformations into a one-dimensional polyhedron and a certain new characteristic of the dimension of sets in Euclidean spaces, Doklady Akad. Nauk SSSR (N.S.) 88 (1953), 21–24 (Russian). MR 0054245