| Title:
|
An approach to covering dimensions (English) |
| Author:
|
Katětov, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
149-169 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively. (English) |
| Keyword:
|
Čech-Lebesgue dimension |
| Keyword:
|
height dimension of posets |
| Keyword:
|
dyadic expansion |
| Keyword:
|
rigged finite open covers |
| Keyword:
|
partition dimension |
| MSC:
|
06A06 |
| MSC:
|
06A10 |
| MSC:
|
54F05 |
| MSC:
|
54F45 |
| idZBL:
|
Zbl 0834.54019 |
| idMR:
|
MR1334423 |
| . |
| Date available:
|
2009-01-08T18:16:43Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118741 |
| . |
| Reference:
|
[A35] Alexandroff P.: Sur les espaces discrets.C.R. Acad. Sci. Paris 200 (1935), 1049-1051. Zbl 0011.32602 |
| Reference:
|
[A37] Alexandroff P.: Diskrete Räume.Mat. Sb. 2 (1937), 501-519. Zbl 0018.09105 |
| Reference:
|
[DM41] Dushnik B., Miller E.W.: Partially ordered sets.Amer. J. Math. 63 (1941), 600-610. Zbl 0025.31002, MR 0004862 |
| Reference:
|
[EDT] Engelking R.: Dimension Theory.Warszawa, 1978. Zbl 0401.54029, MR 0482697 |
| Reference:
|
[EGT] Engelking R.: General Topology.Warszawa, 1977, Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[K52] Katětov M.: On the dimension of non-separable spaces, I. (Russian).Czechosl. Math. J. 77 (1952), 333-368. MR 0061372 |
| Reference:
|
[K92] Katětov M.: Entropy-like functionals: conceptual background and some results.Comment. Math. Univ. Carolinae 33 (1992), 645-660. MR 1240186 |
| Reference:
|
[K93] Katětov M.: Entropies of self-mappings of topological spaces with richer structures.Comment. Math. Univ. Carolinae 34 (1993), 747-768. MR 1263803 |
| Reference:
|
[O71] Ostrand P.A.: Covering dimension in general spaces.General Top. Appl. 1 (1971), 209-221. Zbl 0232.54044, MR 0288741 |
| Reference:
|
[P79] Pol E.: Some examples in the dimension theory of Tychonoff spaces.Fund. Math. 102 (1979), 29-43. Zbl 0398.54024, MR 0525808 |
| Reference:
|
[PP79] Pol E., Pol R.: A hereditarily normal strongly zero-dimensional space containing subspaces of arbitrarily large dimension.Fund. Math. 102 (1979), 137-142. Zbl 0403.54026, MR 0525937 |
| Reference:
|
[Z63] Zarelua V.: On the equality of dimensions (Russian).Mat. Sb. 62 (1963), 295-319. MR 0157352 |
| . |
