Sums of Darboux and continuous functions

Tom 146 / 1995

Juris Steprāns 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.

Autorzy

  • Juris Steprāns

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