Dimension and $\varepsilon $-translations
Goto, Tatsuo
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 803-808 / Harvested from Czech Digital Mathematics Library

Some theorems characterizing the metric and covering dimension of arbitrary subspaces in a Euclidean space will be obtained in terms of $\varepsilon $-translations; some of them were proved in our previous paper [G1] under the additional assumption of the boundedness of subspaces.

Publié le : 1996-01-01
Classification:  54F45,  55M10
@article{118887,
     author = {Tatsuo Goto},
     title = {Dimension and $\varepsilon $-translations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {803-808},
     zbl = {0886.55002},
     mrnumber = {1440710},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118887}
}
Goto, Tatsuo. Dimension and $\varepsilon $-translations. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 803-808. http://gdmltest.u-ga.fr/item/118887/

Alexandroff P.; Hopf H. Topologie, Berlin, Springer-Verlag, 1935. | Zbl 0277.55001

Egorov V.I. On the metric dimension of points of sets (in Russian), Mat. Sb. 48 (1959), 227-250. (1959) | MR 0125563

Engelking R. Dimension Theory, North Holland, 1978. | MR 0482697 | Zbl 0401.54029

Goto T. Metric dimension of bounded subspaces in Euclidean spaces, Top. Proc. 16 (1991), 45-51. (1991) | MR 1206452

Goto T. A construction of a subspace in Euclidean space with designated values of dimension and metric dimension, Proc. Amer. Math. Soc. 118 (1993), 1319-1321. (1993) | MR 1189543 | Zbl 0805.55002

Katětov M. On the dimension of non-separable spaces I (in Russian), Czech. Math. J. 2 (1952), 333-368. (1952) | MR 0061372

Katětov M. On the relation between the metric and topological dimensions (in Russian), Czech. Math. J. 8 (1958), 163-166. (1958) | MR 0105084

Kuratowski K. Topology I, New York, 1966. | Zbl 0849.01044

Sitnikov K. An example of a two dimensional set in three dimensional Euclidean space allowing arbitrarily small deformations into a one dimensional polyhedron and a certain new characterization of the dimension of sets in Euclidean spaces (in Russian), Dokl. Akad. Nauk SSSR 88 (1953), 21-24. (1953) | MR 0054245

Smirnov Ju. On the metric dimension in the sense of P.S. Alexandroff (in Russian), Izv. Akad. Nauk SSSR 20 (1956), 679-684. (1956) | MR 0082096

Smirnov Ju. Geometry of infinite uniform complexes and $\delta $-dimension of points sets, Mat. Sb. 38 (1956), 137-156; Amer. Math. Soc. Transl. Ser. 2, 15 (1960), 95-113. (1956) | MR 0115158

Zarelua A.; Smirnov Ju. Essential and zero-dimensional mappings, Dokl. Nauk SSSR 148 (1963), 1017-1019. (1963) | MR 0157351 | Zbl 0129.38501