# On D-dimension of metrizable spaces

Fundamenta Mathematicae (1991)

- Volume: 140, Issue: 1, page 35-48
- ISSN: 0016-2736

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topOlszewski, Wojciech. "On D-dimension of metrizable spaces." Fundamenta Mathematicae 140.1 (1991): 35-48. <http://eudml.org/doc/211927>.

@article{Olszewski1991,

abstract = {For every cardinal τ and every ordinal α, we construct a metrizable space $M_α(τ)$ and a strongly countable-dimensional compact space $Z_α(τ)$ of weight τ such that $D(M_α(τ)) ≤ α$, $D(Z_α(τ)) ≤ α$ and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of $M_α(τ)$ and to a subspace of $Z_\{α+1\}(τ)$.},

author = {Olszewski, Wojciech},

journal = {Fundamenta Mathematicae},

keywords = {countable-dimensional compact space},

language = {eng},

number = {1},

pages = {35-48},

title = {On D-dimension of metrizable spaces},

url = {http://eudml.org/doc/211927},

volume = {140},

year = {1991},

}

TY - JOUR

AU - Olszewski, Wojciech

TI - On D-dimension of metrizable spaces

JO - Fundamenta Mathematicae

PY - 1991

VL - 140

IS - 1

SP - 35

EP - 48

AB - For every cardinal τ and every ordinal α, we construct a metrizable space $M_α(τ)$ and a strongly countable-dimensional compact space $Z_α(τ)$ of weight τ such that $D(M_α(τ)) ≤ α$, $D(Z_α(τ)) ≤ α$ and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of $M_α(τ)$ and to a subspace of $Z_{α+1}(τ)$.

LA - eng

KW - countable-dimensional compact space

UR - http://eudml.org/doc/211927

ER -

## References

top- [1]R. Engelking, General Topology, Heldermann, Berlin 1989.
- [2]R. Engelking, Dimension Theory, PWN, Warszawa 1978.
- [3] F. Hausdorff, Set Theory, Chelsea, New York 1962.
- [4] D. W. Henderson, D-dimension, I. A new transfinite dimension, Pacific J. Math. 26 (1968), 91-107. Zbl0162.26904
- [5] D. W. Henderson, D-dimension, II. Separable spaces and compactifications, ibid., 109-113. Zbl0162.27001
- [6] I. M. Kozlovskiĭ, Two theorems on metric spaces, Dokl. Akad. Nauk SSSR 204 (1972), 784-787 (in Russian); English transl.: Soviet Math. Dokl. 13 (1972), 743-747. Zbl0268.54030
- [7] L. Luxemburg, On compactifications of metric spaces with transfinite dimension, Pacific J. Math. 101 (1982), 399-450. Zbl0451.54030
- [8] L. Luxemburg, On universal infinite-dimensional spaces, Fund. Math. 122 (1984), 129-147. Zbl0571.54029
- [9] W. Olszewski, Universal spaces for locally finite-dimensional and strongly countable-dimensional metrizable spaces, ibid. 135 (1990), 97-109. Zbl0743.54019
- [10] L. Polkowski, On transfinite dimension, Colloq. Math. 50 (1985), 61-79. Zbl0613.54024
- [11] W. Sierpiński, Cardinal and Ordinal Numbers, PWN, Warszawa 1965.

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