Real Analysis Exchange

Additive Sierpiński-Zygmund functions.

Tomasz Natkaniec and Harvey Rosen

Full-text: Open access

Abstract

In the paper we present an exhaustive discussion of the relations between Darboux-like functions within the class of additive Sierpiński-Zygmund (SZ) functions. In particular, we give an example of an additive Sierpiński-Zygmund (SZ) injection $f : \mathbb{R} \to\mathbb{R}$ such that $f^{-1}$ is not an SZ function. Under the assumption that $\mathbb{R}$ cannot be covered by less than $\mathfrak{c}$-many meager sets we give examples of an additive SZ bijection $f : \mathbb{R} \to\mathbb{R}$ such that $f^{-1}$ is not SZ and of an additive injection $f : \mathbb{R} \to\mathbb{R}$ such that both $f$ and $f^{-1}$ are SZ.

Article information

Source
Real Anal. Exchange, Volume 31, Number 1 (2005), 253-270.

Dates
First available in Project Euclid: 5 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149516806

Mathematical Reviews number (MathSciNet)
MR2218841

Zentralblatt MATH identifier
1110.26002

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
Secondary: 03E50: Continuum hypothesis and Martin's axiom [See also 03E57]

Keywords
additive function Sierpi{\'n}ski-Zygmund function Darboux like function almost continuous functions connectivity functions functions with perfect road peripherally continuous functions CIVP-functions SCIVP-functions

Citation

Natkaniec, Tomasz; Rosen, Harvey. Additive Sierpiński-Zygmund functions. Real Anal. Exchange 31 (2005), no. 1, 253--270. https://projecteuclid.org/euclid.rae/1149516806


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References

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