Sums of Darboux and continuous functions
Tom 146 / 1995
Fundamenta Mathematicae 146 (1995), 107-120
DOI: 10.4064/fm-146-2-107-120
Streszczenie
It is shown that for every Darboux function F there is a non-constant continuous function f such that F + f is still Darboux. It is shown to be consistent - the model used is iterated Sacks forcing - that for every Darboux function F there is a nowhere constant continuous function f such that F + f is still Darboux. This answers questions raised in [5] where it is shown that in various models of set theory there are universally bad Darboux functions, Darboux functions whose sum with any nowhere constant, continuous function fails to be Darboux.
