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: 5

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

Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps

100%
Holický P.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2004
|
tom 52
|
nr 2
151-167
EN
We prove an abstract version of the Kuratowski extension theorem for Borel measurable maps of a given class. It enables us to deduce and improve its nonseparable version due to Hansell. We also study the ranges of not necessarily injective Borel bimeasurable maps f and show that some control on the relative classes of preimages and images of Borel sets under f enables one to get a bound on the absolute class of the range of f. This seems to be of some interest even within separable spaces.
2
Content available remote

Borel sets with σ-compact sections for nonseparable spaces

100%
Holický P.
Fundamenta Mathematicae
|
2008
|
tom 199
|
nr 2
139-154
EN
We prove that every (extended) Borel subset E of X × Y, where X is complete metric and Y is Polish, can be covered by countably many extended Borel sets with compact sections if the sections $E_x = {y ∈ Y: (x,y) ∈ E}$, x ∈ X, are σ-compact. This is a nonseparable version of a theorem of Saint Raymond. As a by-product, we get a proof of Saint Raymond's result which does not use transfinite induction.
3
Content available remote

Borel classes of uniformizations of sets with large sections

100%
Holický P.
Fundamenta Mathematicae
|
2010
|
tom 207
|
nr 2
145-160
EN
We give several refinements of known theorems on Borel uniformizations of sets with "large sections". In particular, we show that a set B ⊂ [0,1] × [0,1] which belongs to $Σ⁰_{α}$, α ≥ 2, and which has all "vertical" sections of positive Lebesgue measure, has a $Π⁰_{α}$ uniformization which is the graph of a $Σ⁰_{α}$-measurable mapping. We get a similar result for sets with nonmeager sections. As a corollary we derive an improvement of Srivastava's theorem on uniformizations for Borel sets with $G_{δ}$ sections.
4
Content available remote

$F_{σ}$-mappings and the invariance of absolute Borel classes

64%
Holický P., Spurný J.
Fundamenta Mathematicae
|
2004
|
tom 182
|
nr 3
193-204
EN
It is proved that $F_{σ}$-mappings preserve absolute Borel classes, which improves results of R. W. Hansell, J. E. Jayne and C. A. Rogers. The proof is based on the fact that any $F_{σ}$-mapping f: X → Y of an absolute Suslin metric space X onto an absolute Suslin metric space Y becomes a piecewise perfect mapping when restricted to a suitable $F_{σ}$-set $X_{∞} ⊂ X$ satisfying $f(X_{∞}) = Y$.
5
Content available remote

C(K) spaces which cannot be uniformly embedded into c₀(Γ)

51%
Pelant J., Holický P., Kalenda O.
Fundamenta Mathematicae
|
2006
|
tom 192
|
nr 3
245-254
EN
We give two examples of scattered compact spaces K such that C(K) is not uniformly homeomorphic to any subset of c₀(Γ) for any set Γ. The first one is [0,ω₁] and hence it has the smallest possible cardinality, the other one has the smallest possible height ω₀ + 1.
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.