Geodesic
Sums of Darboux and continuous functions
Fundamenta Mathematicae, Tome 146 (1994) no. 2, pp. 107-120.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-146-2-107-120

Juris Steprāns 1

1 
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Juris Steprāns. Sums of Darboux and continuous functions. Fundamenta Mathematicae, Tome 146 (1994) no. 2, pp. 107-120. doi : 10.4064/fm-146-2-107-120. http://geodesic.mathdoc.fr/articles/10.4064/fm-146-2-107-120/

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