Sharkovskiĭ's theorem holds for some discontinuous functions

• Autorzy: Piotr Szuca
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 26A21: Classification of real functions; Baire classification of sets and functions
• 37E99: None of the above, but in this section
• 26A18: Iteration
• 54C30: Real-valued functions
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 179
• Numer: 1
• Strony: 27-41

Daty

wydano

2003

Twórcy

autor

Piotr Szuca

• Department of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/fm179-1-3