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: 6

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

The Banach–Mazur game and σ-porosity

100%
Zelený M.
Fundamenta Mathematicae
|
1996
|
tom 150
|
nr 3
197-210
EN
It is well known that the sets of the first category in a metric space can be described using the so-called Banach-Mazur game. We will show that if we change the rules of the Banach-Mazur game (by forcing the second player to choose large balls) then we can describe sets which can be covered by countably many closed uniformly porous sets. A characterization of σ-very porous sets and a sufficient condition for σ-porosity are also given in the terminology of games.
2
Content available remote

A converse of the Arsenin–Kunugui theorem on Borel sets with σ-compact sections

64%
Holický P., Zelený M.
Fundamenta Mathematicae
|
2000
|
tom 165
|
nr 3
191-202
EN
Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel metric) space L onto a metric space M such that f(F) is a Borel subset of M if F is closed in L. We show that then $f^{-1}(y)$ is a $K_σ$ set for all except countably many y ∈ M, that M is also Luzin, and that the Borel classes of the sets f(F), F closed in L, are bounded by a fixed countable ordinal. This gives a converse of the classical theorem of Arsenin and Kunugui. As a particular case we get Taĭmanov's theorem saying that the image of a Luzin space under a closed continuous mapping is a Luzin space. The method is based on a parametrized version of a Hurewicz type theorem and on the use of the Jankov-von Neumann selection theorem.
3
Content available remote

Rudin-like sets and hereditary families of compact sets

64%
Matheron É., Zelený M.
Fundamenta Mathematicae
|
2005
|
tom 185
|
nr 2
97-116
EN
We show that a comeager Π₁¹ hereditary family of compact sets must have a dense $G_δ$ subfamily which is also hereditary. Using this, we prove an "abstract" result which implies the existence of independent ℳ ₀-sets, the meagerness of 𝒰₀-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true $F_{σδ}$ sets.
4
Content available remote

Inscribing compact non-σ-porous sets into analytic non-σ-porous sets

64%
Zelený M., Zajíček L.
Fundamenta Mathematicae
|
2005
|
tom 185
|
nr 1
19-39
EN
The main aim of this paper is to give a simpler proof of the following assertion. Let A be an analytic non-σ-porous subset of a locally compact metric space, E. Then there exists a compact non-σ-porous subset of A. Moreover, we prove the above assertion also for σ-P-porous sets, where P is a porosity-like relation on E satisfying some additional conditions. Our result covers σ-⟨g⟩-porous sets, σ-porous sets, and σ-symmetrically porous sets.
5
Content available remote

Borel chromatic number of closed graphs

64%
Lecomte D., Zelený M.
Fundamenta Mathematicae
|
2016
|
tom 234
|
nr 2
163-169
EN
We construct, for each countable ordinal ξ, a closed graph with Borel chromatic number 2 and Baire class ξ chromatic number ℵ₀.
6
Content available remote

A note on intersections of non-Haar null sets

64%
Matoušková E., Zelený M.
Colloquium Mathematicum
|
2003
|
tom 96
|
nr 1
1-4
EN
We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.
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.