التفاصيل البيبلوغرافية
| العنوان: |
Different notions of Sierpiński–Zygmund functions. |
| المؤلفون: |
Ciesielski, Krzysztof Chris, Natkaniec, Tomasz |
| المصدر: |
Revista Matematica Complutense; 2021, Vol. 34 Issue 1, p151-173, 23p |
| مستخلص: |
A function f : R → R is Sierpiński–Zygmund, f ∈ SZ (C) , provided its restriction f ↾ M is discontinuous for any M ⊂ R of cardinality continuum. Often, it is slightly easier to construct a function f : R → R , denoted as f ∈ SZ (Bor) , with a seemingly stronger property that f ↾ M is not Borel for any M ⊂ R of cardinality continuum. It has been recently noticed that the properness of the inclusion SZ (Bor) ⊆ SZ (C) is independent of ZFC. In this paper we explore the classes SZ (Φ) for arbitrary families Φ of partial functions from R to R . We investigate additivity and lineability coefficients of the class S : = SZ (C) \ SZ (Bor) . In particular we show that if c = κ + and S ≠ ∅ , then the additivity of S is κ , that S is c + -lineable, and it is consistent with ZFC that S is c + + -lineable. We also construct several examples of functions from SZ (C) \ SZ (Bor) that belong also to other important classes of real functions. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
