Dynamics of typical Baire-1 functions on the interval

• Autorzy: Steele T. H.

Identyfikatory

DOI

10.1515/jaa-2017-0009

• Języki publikacji: EN

Abstrakty

EN

Let I = [0, 1], and let bB₁ be the set of Baire-1 self-maps of I. For f ∈ bB₁, let Λ(f) = ⋃_x∈I ω(x, f) be the set of ω-limit points of f . We prove the following: - There exists a residual subset S of bB₁ such that for any f ∈ S and x ∈ I the ω-limit set ω(x, f) is contained in the set of points at which f is continuous, and ω(x, f) is an∞-adic adding machine. - There exists a residual subset S of bB₁ such that for any f ∈ S and for any ε > 0 there exists a natural number M such that f_m (I) ⊂ B_ε(Λ(f)) whenever m > M. Moreover, f : Λ(f) → Λ(f) is a bijection.

Słowa kluczowe

EN

Baire-1 function; omega-limit set; odometer; generic

PL

funkcja pierwszej klasy Baire’a; zbiór omega-graniczny

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2017
• Tom: Vol. 23, nr 2
• Strony: 59--64
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Steele T. H.

• Department of Mathematics, Weber State University, Ogden, UT 84408-2517, USA

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).