On D-dimension of metrizable spaces

Wojciech Olszewski

Fundamenta Mathematicae (1991)

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

Abstract

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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 ) .

How to cite

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Olszewski, 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

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

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