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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The following works have cited this article

**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.

**Last modified January, 2014.**