In the paper we present an exhaust discussion of the relations between Darboux-like functions within the classes of Baire one, Baire two, and additive functions from Rn into R. In particular we construct an additive extendable discontinuous function f:R-->R, answering a question of Gibson and Natkaniec (Darboux like functions, Real Anal. Exchange 22 (1996--97), 492-533), and show that there is no similar function from R2 into R. We also describe a Baire class two almost continuous function f:R-->R which is not extendable. This gives a negative answer to a problem of Brown, Humke, and Laczkovich (Measurable Darboux functions, Proc. Amer. Math. Soc. 102 (1988), 603-610).
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