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1998/1999 Sums of Darboux-Like Functions from ℝn to ℝm
Francis Jordan
Real Anal. Exchange 24(2): 729-760 (1998/1999).


The additivity $A(\mathcal{F})$ of a family $\mathcal{F}\subseteq\mathbb{R}^{\mathbb{R}}$ is the minimum cardinality of a $G\subseteq\mathbb{R}^\mathbb{R}$ with the property that $f+G\subseteq\mathcal{F}$ for no $f\in\mathbb{R}^{\mathbb{R}}$. The values of $A$ have been calculated for many families of Darboux-like functions in $\mathbb{R}^\mathbb{R}$. We extend these results to include some families of Darboux-like functions in $\mathbb{R}^{\mathbb{R}^n}$. To do this we must define $(n,k)$-additivity which is much more flexible than additivity.


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Francis Jordan. "Sums of Darboux-Like Functions from ℝn to ℝm." Real Anal. Exchange 24 (2) 729 - 760, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 28 September 2010

zbMATH: 0967.26009
MathSciNet: MR1704746

Primary: 26A15

Keywords: almost continuous functions , cardinal invariants , connectivity functions , Darboux functions , extendable functions , peripherally continuous functions , Sierpi\'{n}ski-Zygmund functions

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
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