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1
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A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

100%
Marciszewski W.
Fundamenta Mathematicae
|
1997
|
tom 153
|
nr 2
125-40
EN
We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions $c_p(X)$ onto $c_p(X)$ × ℝ$. In particular, $c_p(X)$ is not linearly homeomorphic to $c_p(X)$ × ℝ$. One of these examples is compact. This answers some questions of Arkhangel'skiĭ.
2
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On Banach spaces C(K) isomorphic to c₀(Γ)

100%
Marciszewski W.
Studia Mathematica
|
2003
|
tom 156
|
nr 3
295-302
EN
We give a characterization of compact spaces K such that the Banach space C(K) is isomorphic to the space c₀(Γ) for some set Γ. As an application we show that there exists an Eberlein compact space K of weight $ω_{ω}$ and with the third derived set $K^{(3)}$ empty such that the space C(K) is not isomorphic to any c₀(Γ). For this compactum K, the spaces C(K) and $c₀(ω_{ω})$ are examples of weakly compactly generated (WCG) Banach spaces which are Lipschitz isomorphic but not isomorphic.
3
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Modifications of the double arrow space and related Banach spaces C(K)

100%
Marciszewski W.
Studia Mathematica
|
2008
|
tom 184
|
nr 3
249-262
EN
We consider the class of compact spaces $K_{A}$ which are modifications of the well known double arrow space. The space $K_{A}$ is obtained from a closed subset K of the unit interval [0,1] by "splitting" points from a subset A ⊂ K. The class of all such spaces coincides with the class of separable linearly ordered compact spaces. We prove some results on the topological classification of $K_{A}$ spaces and on the isomorphic classification of the Banach spaces $C(K_{A})$.
4
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On sequential convergence in weakly compact subsets of Banach spaces

100%
Marciszewski W.
Studia Mathematica
|
1994-1995
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tom 112
|
nr 2
189-194
EN
We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.
5
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Some remarks on universality properties of $ℓ_∞/c₀$

64%
Krupski M., Marciszewski W.
Colloquium Mathematicum
|
2012
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tom 128
|
nr 2
187-195
EN
We prove that if 𝔠 is not a Kunen cardinal, then there is a uniform Eberlein compact space K such that the Banach space C(K) does not embed isometrically into $ℓ_∞/c₀$. We prove a similar result for isomorphic embeddings. Our arguments are minor modifications of the proofs of analogous results for Corson compacta obtained by S. Todorčević. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $ℓ_∞/c₀$, but fails to embed isometrically. As far as we know it is the first example of this kind.
6
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Extension operators on balls and on spaces of finite sets

64%
Avilés A., Marciszewski W.
Studia Mathematica
|
2015
|
tom 227
|
nr 2
165-182
EN
We study extension operators between spaces of continuous functions on the spaces $σₙ(2^{X})$ of subsets of X of cardinality at most n. As an application, we show that if $B_{H}$ is the unit ball of a nonseparable Hilbert space H equipped with the weak topology, then, for any 0 < λ < μ, there is no extension operator $T: C(λB_{H}) → C(μB_{H})$.
7
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Failure of the Factor Theorem for Borel pre-Hilbert spaces

64%
Dobrowolski T., Marciszewski W.
Fundamenta Mathematicae
|
2002
|
tom 175
|
nr 1
53-68
EN
In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an $F_{σδσ}$-subset of X and contains a retract R so that $R × E^{ω}$ is not homeomorphic to $E^{ω}$. This shows that Toruńczyk's Factor Theorem fails in the Borel case.
8
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A contribution to the topological classification of the spaces Ср(X)

51%
Cauty R., Dobrowolski T., Marciszewski W.
Fundamenta Mathematicae
|
1993
|
tom 142
|
nr 3
269-301
EN
We prove that for each countably infinite, regular space X such that $C_p(X)$ is a $Z_σ$-space, the topology of $C_p(X)$ is determined by the class $F_0(C_p(X))$ of spaces embeddable onto closed subsets of $C_p(X)$. We show that $C_p(X)$, whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set $Ω_α$ for the multiplicative Borel class $M_α$ if $F_0(C_p(X)) = M_α$. For each ordinal α ≥ 2, we provide an example $X_α$ such that $C_p(X_α)$ is homeomorphic to $Ω_α$.
9
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Classification of function spaces with the pointwise topology determined by a countable dense set

51%
Dobrowolski T., Marciszewski W.
Fundamenta Mathematicae
|
1995
|
tom 148
|
nr 1
35-62
10
Content available remote

On a classification of pointwise compact sets of the first Baire class functions

50%
Marciszewski W.
Fundamenta Mathematicae
|
1989
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tom 133
|
nr 3
195-209
11
Content available remote

A function space C(K) not weakly homeomorphic to C(K)×C(K)

38%
Marciszewski W.
Studia Mathematica
|
1988
|
tom 88
|
nr 2
129-137
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