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 Covering Principle for Darboux Baire 1 functions

100%
Szuca P.
Fundamenta Mathematicae
|
2007
|
tom 193
|
nr 2
133-140
EN
We show that the Covering Principle known for continuous maps of the real line also holds for functions whose graph is a connected $G_{δ}$ subset of the plane. As an application we find an example of an approximately continuous (hence Darboux Baire 1) function f: [0,1] → [0,1] such that any closed subset of [0,1] can be translated so as to become an ω-limit set of f. This solves a problem posed by Bruckner, Ceder and Pearson [Real Anal. Exchange 15 (1989/90)].
2
Content available remote

F-limit points in dynamical systems defined on the interval

100%
Szuca P.
Open Mathematics
|
2013
|
tom 11
|
nr 1
170-176
EN
Given a free ultrafilter p on ℕ we say that x ∈ [0, 1] is the p-limit point of a sequence (x n)n∈ℕ ⊂ [0, 1] (in symbols, x = p -limn∈ℕ x n) if for every neighbourhood V of x, {n ∈ ℕ: x n ∈ V} ∈ p. For a function f: [0, 1] → [0, 1] the function f p: [0, 1] → [0, 1] is defined by f p(x) = p -limn∈ℕ f n(x) for each x ∈ [0, 1]. This map is rarely continuous. In this note we study properties which are equivalent to the continuity of f p. For a filter F we also define the ω F-limit set of f at x. We consider a question about continuity of the multivalued map x → ω fF(x). We point out some connections between the Baire class of f p and tame dynamical systems, and give some open problems.
3
Content available remote

Sharkovskiĭ's theorem holds for some discontinuous functions

100%
Szuca P.
Fundamenta Mathematicae
|
2003
|
tom 179
|
nr 1
27-41
EN
We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected $G_δ$ graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected $G_δ$ graph.
4
Content available remote

On the ideal convergence of sequences of quasi-continuous functions

64%
Natkaniec T., Szuca P.
Fundamenta Mathematicae
|
2016
|
tom 232
|
nr 3
269-280
EN
For any Borel ideal ℐ we describe the ℐ-Baire system generated by the family of quasi-continuous real-valued functions. We characterize the Borel ideals ℐ for which the ideal and ordinary Baire systems coincide.
5
Content available remote

On Pawlak's problem concerning entropy of almost continuous functions

64%
Natkaniec T., Szuca P.
Colloquium Mathematicum
|
2010
|
tom 121
|
nr 1
107-111
EN
We prove that if f:𝕀 → 𝕀 is Darboux and has a point of prime period different from $2^i$, i = 0,1,..., then the entropy of f is positive. On the other hand, for every set A ⊂ ℕ with 1 ∈ A there is an almost continuous (in the sense of Stallings) function f:𝕀 → 𝕀 with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.
6
Content available remote

When does the Katětov order imply that one ideal extends the other?

51%
Barbarski P., Filipów R., Mrożek N., Szuca P.
Colloquium Mathematicum
|
2013
|
tom 130
|
nr 1
91-102
EN
We consider the Katětov order between ideals of subsets of natural numbers ("$≤_{K}$") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals 𝓘 for which $𝓘 ≤_{K} 𝒥 ⇒ 𝓘 ⊑ 𝒥$ for every ideal 𝒥. We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).
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.