An approach to covering dimensions

Miroslav Katětov

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 1, page 149-169
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Katětov, 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

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  3. Dushnik B., Miller E.W., Partially ordered sets, Amer. J. Math. 63 (1941), 600-610. (1941) Zbl0025.31002MR0004862
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  7. Katětov M., Entropy-like functionals: conceptual background and some results, Comment. Math. Univ. Carolinae 33 (1992), 645-660. (1992) MR1240186
  8. Katětov M., Entropies of self-mappings of topological spaces with richer structures, Comment. Math. Univ. Carolinae 34 (1993), 747-768. (1993) MR1263803
  9. Ostrand P.A., Covering dimension in general spaces, General Top. Appl. 1 (1971), 209-221. (1971) Zbl0232.54044MR0288741
  10. Pol E., Some examples in the dimension theory of Tychonoff spaces, Fund. Math. 102 (1979), 29-43. (1979) Zbl0398.54024MR0525808
  11. 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
  12. Zarelua V., On the equality of dimensions (Russian), Mat. Sb. 62 (1963), 295-319. (1963) MR0157352

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