Eberly College of Arts and Sciences
In this note we will construct several additive Darboux-like functions f : R → R answering some problems from (an earlier version of) . 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.
Digital Commons Citation
Ciesielski, Krzysztof, "Some Additive Darboux-like functions" (1998). Faculty & Staff Scholarship. 832.