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Sum of Sierpiński–Zygmund and Darboux like functions by Krzysztof Płotka is a Mathematics article available to read on EtoBox.
What is Sum of Sierpiński–Zygmund and Darboux like functions about?
For F 1 , F 2 ⊆ R R we define Add(F 1 , F 2 ) as the smallest cardinality of a family F ⊆ R R for which there is no g ∈ F 1 such that g + F ⊆ F 2 . The main goal of this note is to investigate the function Add in the case when one of the classes F 1 , F 2 is the class SZ of Sierpiński-Zygmund functions. In particular, we show that Martin's Axiom (MA) implies Add(AC, SZ) ω and Add(SZ, AC) = Add(SZ, D) = c, where AC and D denote the families of almost continuous and Darboux functions, respectively. As a corollary we obtain that the proposition, every function from R into R can be represented as a sum of Sierpiński-Zygmund and almost continuous functions, is independent of ZFC axioms.
Who reads Sum of Sierpiński–Zygmund and Darboux like functions?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Krzysztof Płotka
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-8641)
- Published
- 2002
- Language
- EN
- Field
- Mathematics (Physical Sciences)