An approach to covering dimensions
Commentationes Mathematicae Universitatis Carolinae (1995)
- Volume: 36, Issue: 1, page 149-169
- ISSN: 0010-2628
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topKatětov, Miroslav. "An approach to covering dimensions." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 149-169. <http://eudml.org/doc/247716>.
@article{Katětov1995,
abstract = {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.},
author = {Katětov, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Čech-Lebesgue dimension; height dimension of posets; dyadic expansion; rigged finite open covers; partition dimension; Čech-Lebesgue dimension},
language = {eng},
number = {1},
pages = {149-169},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An approach to covering dimensions},
url = {http://eudml.org/doc/247716},
volume = {36},
year = {1995},
}
TY - JOUR
AU - Katětov, Miroslav
TI - An approach to covering dimensions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 149
EP - 169
AB - 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.
LA - eng
KW - Čech-Lebesgue dimension; height dimension of posets; dyadic expansion; rigged finite open covers; partition dimension; Čech-Lebesgue dimension
UR - http://eudml.org/doc/247716
ER -
References
top- Alexandroff P., Sur les espaces discrets, C.R. Acad. Sci. Paris 200 (1935), 1049-1051. (1935) Zbl0011.32602
- Alexandroff P., Diskrete Räume, Mat. Sb. 2 (1937), 501-519. (1937) Zbl0018.09105
- Dushnik B., Miller E.W., Partially ordered sets, Amer. J. Math. 63 (1941), 600-610. (1941) Zbl0025.31002MR0004862
- Engelking R., Dimension Theory, Warszawa, 1978. Zbl0401.54029MR0482697
- Engelking R., General Topology, Warszawa, 1977, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
- Katětov M., On the dimension of non-separable spaces, I. (Russian), Czechosl. Math. J. 77 (1952), 333-368. (1952) MR0061372
- Katětov M., Entropy-like functionals: conceptual background and some results, Comment. Math. Univ. Carolinae 33 (1992), 645-660. (1992) MR1240186
- Katětov M., Entropies of self-mappings of topological spaces with richer structures, Comment. Math. Univ. Carolinae 34 (1993), 747-768. (1993) MR1263803
- Ostrand P.A., Covering dimension in general spaces, General Top. Appl. 1 (1971), 209-221. (1971) Zbl0232.54044MR0288741
- Pol E., Some examples in the dimension theory of Tychonoff spaces, Fund. Math. 102 (1979), 29-43. (1979) Zbl0398.54024MR0525808
- Pol E., Pol R., A hereditarily normal strongly zero-dimensional space containing subspaces of arbitrarily large dimension, Fund. Math. 102 (1979), 137-142. (1979) Zbl0403.54026MR0525937
- Zarelua V., On the equality of dimensions (Russian), Mat. Sb. 62 (1963), 295-319. (1963) MR0157352
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