Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 11

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

On Convex Sets with Convex-Hereditary CEP

100%
Dobrowolski T.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2011
|
tom 59
|
nr 3
215-222
EN
CEP stands for the compact extension property. We characterize nonlocally convex complete metric linear spaces with convex-hereditary CEP.
2
Content available remote

A Polish AR-Space with no Nontrivial Isotopy

100%
Dobrowolski T.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2008
|
tom 56
|
nr 1
67-74
EN
The Polish space Y constructed in [vM1] admits no nontrivial isotopy. Yet, there exists a Polish group that acts transitively on Y.
3
Content available remote

Selections and near-selections in metric linear spaces without local convexity

64%
Dobrowolski T., van Mill J.
Fundamenta Mathematicae
|
2006
|
tom 192
|
nr 3
215-232
EN
We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
4
Content available remote

The space of ANR’s in $ℝ^n$

64%
Dobrowolski T., Rubin L. R.
Fundamenta Mathematicae
|
1994-1995
|
tom 146
|
nr 1
31-58
EN
The hyperspaces $ANR(ℝ^n)$ and $AR(ℝ^n)$ in $2^{ℝ^n} (n ≥ 3)$ consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute $G_{δσ δ}$-spaces and that, indeed, they are not $F_{σ δσ }$-spaces. The main result is that $ANR(ℝ^n)$ is an absorber for the class of all absolute $G_{δσ δ}$-spaces and is therefore homeomorphic to the standard model space $Ω_3$ of this class.
5
Content available remote

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.
6
Content available remote

Applications of some results of infinite-dimensional topology to the topological classification of operator images

57%
Banakh T., Dobrowolski T., Plichko A.
Instytut Matematyczny Polskiej Akademii Nauk
EN
This volume consists of three relatively independent articles devoted to the topological study of the so-called operator images and weak unit balls of Banach spaces. These articles are: "The topological classification of weak unit balls of Banach spaces" by T. Banakh, "The topological and Borel classification of operator images" by T. Banakh, T. Dobrowolski and A. Plichko, and "Operator images homeomorphic to $Σ^{ω}$" by T. Banakh. The articles summarize investigations that has been done by these authors for the past 10 years. All that started in the late 80s with the following question by T. Dobrowolski: Is the topological type of an operator image fully determined by its Borel type? Let us recall that an operator image is a space of the form TX, where T:X → Y is a continuous linear operator between Fréchet spaces (operator images often appear in analysis and topology, for example, the space $C_{p}*(X)$ of bounded continuous functions on a countable space X with the topology of pointwise convergence can be considered as an operator image of the Banach space C(βX)). In the early 90s T. Dobrowolski obtained a positive answer to the above question for operator images of low Borel complexity. Namely, he showed that every infinite-dimensional separable σ-complete operator image is homeomorphic to one of the spaces: l², Σ, or Σ × l², where Σ is the linear hull of the standard Hilbert cube in the Hilbert space l² (a space is σ-complete if it is a countable union of closed completely-metrizable subspaces). The same result was proved independently by T. Banakh. The topological structure of operator images of higher Borel complexity remained unclear. However, it was known that the topological type of $C_{p}*(X)$ is determined by its Borel type for the case of the second multiplicative Borel class. More precisely, each absolute $F_{σδ}$-space $C_{p}*(X)$ over a nondiscrete space X is homeomorphic to $Σ^{ω}$. Thus the conjecture appeared: The spaces l², Σ, Σ × l² and $Σ^{ω}$ exhaust all possible topological types of infinite-dimensional operator images that are absolute $F_{σδ}$-spaces. Numerous attempts to confirm this conjecture were unsuccessful (though many of those attempts lead to very fruitful developments in infinite-dimensional topology). Finally, in 1998, T. Banakh found a counterexample to the above conjecture. The counterexample came from the study of the weak topology of the closed unit balls of Banach spaces. It turned out that the topological type of an operator image TX depends much on the geometric properties of the Fréchet space X as well as on the properties of the weak topology of X. This topic, which is of independent interest, is considered in detail in the first article of this volume, that is, "The topological classification of weak unit balls of Banach spaces". An example of a pathological Banach space constructed in the last section of this article is applied in the remaining two articles, strictly devoted to studying operator images. The first of them, "The topological and Borel classification of operator images", deals with some general questions in the area, and also with operator images of high Borel complexity, while the second one is restricted to the study of operator images homeomorphic to $Σ^{ω}$. We refer the reader to Introductions that the three articles start with for more detailed information on their contents.
7
Content available remote

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 $Ω_α$.
8
Content available remote

Closed subgroups in Banach spaces

51%
D. Ancel F., Dobrowolski T., Grabowski J.
Studia Mathematica
|
1994
|
tom 109
|
nr 3
277-290
EN
We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of $c_0$. Other results on subgroups of linear spaces are obtained.
9
Content available remote

Topological type of weakly closed subgroups in Banach spaces

51%
Dobrowolski T., Grabowski J., Kawamura K.
Studia Mathematica
|
1996
|
tom 118
|
nr 1
49-62
EN
The main result says that nondiscrete, weakly closed, containing no nontrivial linear subspaces, additive subgroups in separable reflexive Banach spaces are homeomorphic to the complete Erdős space. Two examples of such subgroups in $ℓ^1$ which are interesting from the Banach space theory point of view are discussed.
10
Content available remote

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
11
Content available remote

Les hyperespaces des rétractes absolus et des rétractes absolus de voisinage du plan

45%
Cauty R., Dobrowolski T., Gladdines H., van Mill J.
Fundamenta Mathematicae
|
1995
|
tom 148
|
nr 3
257-282
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.