In this paper we introduce and examine a cardinal invariant $A$_b closely connected to the addition of bounded functions from R to R. It is analogous to the invariant A defined earlier for arbitrary functions by T. Natkaniec. In particular, it is proved that each bounded function can be written as the sum of two bounded almost continuous functions, and an example is given that there is a bounded function which cannot be expressed as the sum of two bounded extendable functions.

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Journal Articles

H. Rosen, Every real function is the sum of two extendable connectivity functions, Real Anal. Exchange 21(1) (1996), 299--303.

K. Ciesielski, Set Theoretic Real Analysis, J. Appl. Anal. 3(2) (1997), 143-190. MR 99k:03038

R. G. Gibson and T. Natkaniec, Darboux like functions, Real Anal. Exchange 22(2) (1997), 492--533.

A. Maliszewski, Darboux Property and Quasi-continuity: a uniform approach, Pedagogical University, Slupsk, Poland, 1996.

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