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  1. 5 Fundamenta Mathematicae

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  1. 5 Olszewski W.

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  1. 3 1994

  2. 1 1991

  3. 1 1990

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1
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Universal spaces in the theory of transfinite dimension, I

100%
Olszewski W.
Fundamenta Mathematicae
|
1994
|
tom 144
|
nr 3
243-258
EN
R. Pol has shown that for every countable ordinal α, there exists a universal space for separable metrizable spaces X with ind X = α . We prove that for every countable limit ordinal λ, there is no universal space for separable metrizable spaces X with Ind X = λ. This implies that there is no universal space for compact metrizable spaces X with Ind X = λ. We also prove that there is no universal space for compact metrizable spaces X with ind X = λ.
2
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Cantor manifolds in the theory of transfinite dimension

100%
Olszewski W.
Fundamenta Mathematicae
|
1994
|
tom 145
|
nr 1
39-64
EN
For every countable non-limit ordinal α we construct an α-dimensional Cantor ind-manifold, i.e., a compact metrizable space $Z_α$ such that $ind Z_α = α$, and no closed subset L of $Z_α$ with ind L less than the predecessor of α is a partition in $Z_α$. An α-dimensional Cantor Ind-manifold can be constructed similarly.
3
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Universal spaces in the theory of transfinite dimension, II

100%
Olszewski W.
Fundamenta Mathematicae
|
1994
|
tom 145
|
nr 2
121-139
EN
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.
4
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On D-dimension of metrizable spaces

100%
Olszewski W.
Fundamenta Mathematicae
|
1991-1992
|
tom 140
|
nr 1
35-48
EN
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 $Z_{α+1}(τ)$.
5
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Universal spaces for locally finite-dimensional and strongly countable-dimensional metrizable spaces

63%
Olszewski W.
Fundamenta Mathematicae
|
1990
|
tom 135
|
nr 2
97-109
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