Dimension and ε -translations

Tatsuo Goto

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 4, page 803-808
  • ISSN: 0010-2628

Abstract

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

How to cite

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Goto, Tatsuo. "Dimension and $\varepsilon $-translations." Commentationes Mathematicae Universitatis Carolinae 37.4 (1996): 803-808. <http://eudml.org/doc/247874>.

@article{Goto1996,
abstract = {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.},
author = {Goto, Tatsuo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {metric dimension; covering dimension; $\varepsilon $-translation; uniformly $0$-dimensional mappings; metric dimension; covering dimension; -translation; uniformly 0-dimensional mappings},
language = {eng},
number = {4},
pages = {803-808},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Dimension and $\varepsilon $-translations},
url = {http://eudml.org/doc/247874},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Goto, Tatsuo
TI - Dimension and $\varepsilon $-translations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 4
SP - 803
EP - 808
AB - 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.
LA - eng
KW - metric dimension; covering dimension; $\varepsilon $-translation; uniformly $0$-dimensional mappings; metric dimension; covering dimension; -translation; uniformly 0-dimensional mappings
UR - http://eudml.org/doc/247874
ER -

References

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  1. Alexandroff P., Hopf H., Topologie, Berlin, Springer-Verlag, 1935. Zbl0277.55001
  2. Egorov V.I., On the metric dimension of points of sets (in Russian), Mat. Sb. 48 (1959), 227-250. (1959) MR0125563
  3. Engelking R., Dimension Theory, North Holland, 1978. Zbl0401.54029MR0482697
  4. Goto T., Metric dimension of bounded subspaces in Euclidean spaces, Top. Proc. 16 (1991), 45-51. (1991) MR1206452
  5. 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) Zbl0805.55002MR1189543
  6. Katětov M., On the dimension of non-separable spaces I (in Russian), Czech. Math. J. 2 (1952), 333-368. (1952) MR0061372
  7. Katětov M., On the relation between the metric and topological dimensions (in Russian), Czech. Math. J. 8 (1958), 163-166. (1958) MR0105084
  8. Kuratowski K., Topology I, New York, 1966. Zbl0849.01044
  9. 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) MR0054245
  10. Smirnov Ju., On the metric dimension in the sense of P.S. Alexandroff (in Russian), Izv. Akad. Nauk SSSR 20 (1956), 679-684. (1956) MR0082096
  11. Smirnov Ju., Geometry of infinite uniform complexes and δ -dimension of points sets, Mat. Sb. 38 (1956), 137-156; Amer. Math. Soc. Transl. Ser. 2, 15 (1960), 95-113. (1956) MR0115158
  12. Zarelua A., Smirnov Ju., Essential and zero-dimensional mappings, Dokl. Nauk SSSR 148 (1963), 1017-1019. (1963) Zbl0129.38501MR0157351

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