The Covering Principle for Darboux Baire 1 functions

• Autorzy: Piotr Szuca
• Języki publikacji: EN

Abstrakty

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)].

Kategorie tematyczne

• 26A21: Classification of real functions; Baire classification of sets and functions
• 26A18: Iteration
• 54C30: Real-valued functions
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 193
• Numer: 2
• Strony: 133-140

Daty

wydano

2007

Twórcy

autor

Piotr Szuca

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

Identyfikatory

DOI

10.4064/fm193-2-2