Open Access
1996/1997 Cardinal invariants connected with adding real functions
Francis Jordan
Author Affiliations +
Real Anal. Exchange 22(2): 696-713 (1996/1997).


In this paper we consider a cardinal invariant related to adding real functions defined on the real line. Let \(\mathcal{F}\) be such a family, we consider the smallest cardinality of a family \(\mathcal{G}\) of functions such that \(h+\mathcal{G}\) has non-empty intersection with \(\mathcal{F}\) for every function \(h\). We note that this cardinal is the additivity, a cardinal previously studied, of the compliment of \(\mathcal{F}\). Thus, we calculate the additivities of the compliments of various families of functions including the Darboux, almost continuous, extendable and perfect road functions. We briefly consider the general relationship between the additivity of a family and its compliment.


Download Citation

Francis Jordan. "Cardinal invariants connected with adding real functions." Real Anal. Exchange 22 (2) 696 - 713, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 22 May 2012

zbMATH: 0942.26005
MathSciNet: MR1460982

Primary: 26A15 , 54A25.
Secondary: 03E75

Keywords: almost continuous , cardinal invariants; extendable , Darboux , perfect road , peripherially continuous

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 2 • 1996/1997
Back to Top