On sums of Darboux and nowhere constant continuous functions
by
Krzysztof Ciesielski,
and J. Pawlikowski
Proc. Amer. Math. Soc. 130(7) (2002), 20072013.
We show that the property
 for every Darboux function g:R>R there exists
a continuous nowhere constant function f:R>R such that f+g is Darboux
follows from the following two propositions:

for every subset S of R of cardinality
continuum there exists a uniformly continuous
function f:R>[0,1] such that f[S]=[0,1],

for an arbitrary function h:R>R whose
image h[R] contains a nontrivial interval
there exists a subset A of R of cardinality
continuum such that the restriction hA of h to A
is uniformly continuous,
which hold in the iterated perfect set model.
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Last modified March 30, 2002.