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Some Additive Darboux–Like Functions
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K. Ciesielski
Veröffentlicht/Copyright:
4. Juni 2010
Abstract
In this note we will construct several additive Darboux-like functions ƒ : ℝ → ℝ answering some problems from (an earlier version of) [Gibson, Natkaniec, Real Anal. Exchange, 22: 492–533, 1996–97]. In particular, in Section 2 we will construct, under different additional set theoretical assumptions, additive almost continuous (in sense of Stallings) functions ƒ : ℝ → ℝ whose graph is either meager or null in the plane. In Section 3 we will construct an additive almost continuous function ƒ : ℝ → ℝ which has the Cantor intermediate value property but is discontinuous on any perfect set. In particular, such an ƒ does not have the strong Cantor intermediate value property.
Received: 1997-06-11
Revised: 1997-09-16
Published Online: 2010-06-04
Published in Print: 1998-June
© Heldermann Verlag
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- Some Additive Darboux–Like Functions
- New Existence Theorems for Solutions of Generalized Quasi–Variational Inequalities
- Oscillatory Properties of the Solutions of Impulsive Differential Equations with Retarded Argument and Oscillating Coefficients
- Set–Valued Implicit Wiener-Hopf Equations and Generalized Strongly Nonlinear Quasivariational Inequalities
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Artikel in diesem Heft
- The Lifting Problem with the Full Ideal
- Contrasting Symmetric Porosity and Porosity
- Some Additive Darboux–Like Functions
- New Existence Theorems for Solutions of Generalized Quasi–Variational Inequalities
- Oscillatory Properties of the Solutions of Impulsive Differential Equations with Retarded Argument and Oscillating Coefficients
- Set–Valued Implicit Wiener-Hopf Equations and Generalized Strongly Nonlinear Quasivariational Inequalities
- Selfgravitating Electrodynamic Stability of a Fluid-Tar Annular Jet Pervaded by Periodic Time Dependet Electric Field
- The Cauchy Problem for the Einstein–Vlasov System
- The Cauchy Problem for the Einstein–Boltzmann System
