| Title:
|
Dimension and $\varepsilon $-translations (English) |
| Author:
|
Goto, Tatsuo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
803-808 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
metric dimension |
| Keyword:
|
covering dimension |
| Keyword:
|
$\varepsilon $-translation |
| Keyword:
|
uniformly $0$-dimensional mappings |
| MSC:
|
54F45 |
| MSC:
|
55M10 |
| idZBL:
|
Zbl 0886.55002 |
| idMR:
|
MR1440710 |
| . |
| Date available:
|
2009-01-08T18:28:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118887 |
| . |
| Reference:
|
[AH] Alexandroff P., Hopf H.: Topologie.Berlin, Springer-Verlag, 1935. Zbl 0277.55001 |
| Reference:
|
[Eg] Egorov V.I.: On the metric dimension of points of sets (in Russian).Mat. Sb. 48 (1959), 227-250. MR 0125563 |
| Reference:
|
[E] Engelking R.: Dimension Theory.North Holland, 1978. Zbl 0401.54029, MR 0482697 |
| Reference:
|
[G1] Goto T.: Metric dimension of bounded subspaces in Euclidean spaces.Top. Proc. 16 (1991), 45-51. MR 1206452 |
| Reference:
|
[G2] 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. Zbl 0805.55002, MR 1189543 |
| Reference:
|
[Ka1] Katětov M.: On the dimension of non-separable spaces I (in Russian).Czech. Math. J. 2 (1952), 333-368. MR 0061372 |
| Reference:
|
[Ka2] Katětov M.: On the relation between the metric and topological dimensions (in Russian).Czech. Math. J. 8 (1958), 163-166. MR 0105084 |
| Reference:
|
[Ku] Kuratowski K.: Topology I.New York, 1966. Zbl 0849.01044 |
| Reference:
|
[S] 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. MR 0054245 |
| Reference:
|
[Sm1] Smirnov Ju.: On the metric dimension in the sense of P.S. Alexandroff (in Russian).Izv. Akad. Nauk SSSR 20 (1956), 679-684. MR 0082096 |
| Reference:
|
[Sm2] 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. MR 0115158 |
| Reference:
|
[Z-S] Zarelua A., Smirnov Ju.: Essential and zero-dimensional mappings.Dokl. Nauk SSSR 148 (1963), 1017-1019. Zbl 0129.38501, MR 0157351 |
| . |
