Universal spaces in the theory of transfinite dimension, II
Fundamenta Mathematicae (1994)
- Volume: 145, Issue: 2, page 121-139
- ISSN: 0016-2736
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Abstract
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topOlszewski, Wojciech. "Universal spaces in the theory of transfinite dimension, II." Fundamenta Mathematicae 145.2 (1994): 121-139. <http://eudml.org/doc/212038>.
@article{Olszewski1994,
abstract = {We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension $ω_0$, or, equivalently, of small transfinite dimension $ω_0$; that is, the family consists of compact metrizable spaces whose transfinite dimension is $ω_0$, and every compact metrizable space with transfinite dimension $ω_0$ is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the least possible cardinality of a dominating sequence of irrational numbers.},
author = {Olszewski, Wojciech},
journal = {Fundamenta Mathematicae},
keywords = {universal space; universal family},
language = {eng},
number = {2},
pages = {121-139},
title = {Universal spaces in the theory of transfinite dimension, II},
url = {http://eudml.org/doc/212038},
volume = {145},
year = {1994},
}
TY - JOUR
AU - Olszewski, Wojciech
TI - Universal spaces in the theory of transfinite dimension, II
JO - Fundamenta Mathematicae
PY - 1994
VL - 145
IS - 2
SP - 121
EP - 139
AB - We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension $ω_0$, or, equivalently, of small transfinite dimension $ω_0$; that is, the family consists of compact metrizable spaces whose transfinite dimension is $ω_0$, and every compact metrizable space with transfinite dimension $ω_0$ is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the least possible cardinality of a dominating sequence of irrational numbers.
LA - eng
KW - universal space; universal family
UR - http://eudml.org/doc/212038
ER -
References
top- [1] E. K. van Douwen, The Integers and Topology, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 111-167.
- [2] R. Engelking, Dimension Theory, PWN, Warszawa, 1978.
- [3] R. Engelking, Transfinite dimension, in: Surveys in General Topology, G. M. Reed (ed.), Academic Press, 1980, 131-161.
- [4] R. Engelking, General Topology, Heldermann, Berlin, 1989.
- [5] L. A. Luxemburg, On transfinite inductive dimensions, Dokl. Akad. Nauk SSSR 209 (1973), 295-298 (in Russian); English transl.: Soviet Math. Dokl. 14 (1973), 388-393. Zbl0283.54019
- [6] L. A. Luxemburg, On compactifications of metric spaces with transfinite dimensions, Pacific J. Math. 101 (1982), 399-450. Zbl0451.54030
- [7] W. Olszewski, Universal spaces for locally finite-dimensional and strongly countable-dimensional metrizable spaces, Fund. Math. 135 (1990), 97-109. Zbl0743.54019
- [8] W. Olszewski, Universal spaces in the theory of transfinite dimension, I, ibid. 144 (1994), 243-258. Zbl0812.54041
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