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Covering Baire 1 Functions with Darboux Functions and the Cofinality of the Ideal of Meager Sets
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F. Jordan
Published/Copyright:
June 4, 2010
Abstract
Let Dar stand for the Darboux Baire class 1 functions. We show that the cofinality of the meager sets in ℝ is the smallest cardinality of a set of Baire class 1 functions F such that for any finite collection of Baire class 1 functions G there is an ƒ ∈ F such that ƒ + G ⊆ Dar. Other results of this type are shown. These results are then considered as statements about additivity. The notion of super–additivity is introduced.
Key words and phrases.: Cardinal functions; meager sets; Baire class 1; extendable functions; connectivity functions; peripherially continuous functions; almost continuous functions; Darboux functions
Received: 1998-02-02
Revised: 1998-09-23
Published Online: 2010-06-04
Published in Print: 1999-June
© Heldermann Verlag
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Articles in the same Issue
- Oscillation Criteria for a Class of Functional Parabolic Equations
- Singular Filters for the Radon Backprojection
- Chemical Attack in Free Boundary Domains
- On Minimax Inequality and Generalized Quasi–Variational Inequality in H-Spaces
- Covering Baire 1 Functions with Darboux Functions and the Cofinality of the Ideal of Meager Sets
- On a Type of Hyperbolic Variational–Hemivariational Inequalities
- A Coloring Result for the Plane
- Nonlinear Alternative: Application to an Integral Equation
- Multivariable Regular Variation of Functions and Measures
- Constrained Equilibrium Point of Maximal Monotone Operator Via Variational Inequality
