In this note we will construct several additive
Darboux-like functions f:**R**-->**R**
answering some problems from (an earlier version of) a survey
Darboux like functions by
R.G.Gibson and T.Natkaniec.
In particular,
in Section 2 we will construct, under different
additional set theoretical assumptions,
additive almost continuous (in sense of Stallings)
functions f:**R**-->**R** whose graph is either meager or null
in the plane.
In Section 3 we will construct
an additive almost continuous function f:**R**-->**R**
which has the Cantor intermediate value property
but is discontinuous on any perfect set. In particular, such an f
does not have the strong Cantor intermediate value property.

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**Last modified January 28, 2007.**