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1
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Quotients of Banach spaces and surjectively universal spaces

100%
Dodos P.
Studia Mathematica
|
2010
|
tom 197
|
nr 2
171-194
EN
We characterize those classes 𝓒 of separable Banach spaces for which there exists a separable Banach space Y not containing ℓ₁ and such that every space in the class 𝓒 is a quotient of Y.
2
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Stable families of analytic sets

100%
Dodos P.
Colloquium Mathematicum
|
2003
|
tom 98
|
nr 2
277-281
EN
We give a different proof of the well-known fact that any uncountable family of analytic subsets of a Polish space with the point-finite intersection property must contain a subfamily whose union is not analytic. Our approach is based on the Kunen-Martin theorem.
3
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On certain regularity properties of Haar-null sets

100%
Dodos P.
Fundamenta Mathematicae
|
2004
|
tom 181
|
nr 2
97-109
EN
Let X be an abelian Polish group. For every analytic Haar-null set A ⊆ X let T(A) be the set of test measures of A. We show that T(A) is always dense and co-analytic in P(X). We prove that if A is compact then T(A) is $G_δ$ dense, while if A is non-meager then T(A) is meager. We also strengthen a result of Solecki and we show that for every analytic Haar-null set A, there exists a Borel Haar-null set B ⊇ A such that T(A)∖ T(B) is meager. Finally, under Martin's Axiom and the negation of Continuum Hypothesis, some results concerning co-analytic sets are derived.
4
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Ranks for baire multifunctions

100%
Dodos P.
Colloquium Mathematicum
|
2003
|
tom 95
|
nr 1
63-77
EN
Various ordinal ranks for Baire-1 real-valued functions, which have been used in the literature, are adapted to provide ranks for Baire-1 multifunctions. A new rank is also introduced which, roughly speaking, gives an estimate of how far a Baire-1 multifunction is from being upper semicontinuous.
5
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A strong boundedness result for separable Rosenthal compacta

100%
Dodos P.
Fundamenta Mathematicae
|
2008
|
tom 198
|
nr 2
177-189
EN
It is proved that the class of separable Rosenthal compacta on the Cantor set having a uniformly bounded dense sequence of continuous functions is strongly bounded.
6
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Some strongly bounded classes of Banach spaces

64%
Dodos P., Ferenczi V.
Fundamenta Mathematicae
|
2007
|
tom 193
|
nr 2
171-179
EN
We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach space.
7
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On unconditionally saturated Banach spaces

64%
Dodos P., Lopez-Abad J.
Studia Mathematica
|
2008
|
tom 188
|
nr 2
175-191
EN
We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set 𝓐, in the Effros-Borel space of subspaces of C[0,1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y, with a Schauder basis, that contains isomorphic copies of every space X in the class 𝓐.
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