On sums of Darboux and nowhere constant continuous functions
and J. Pawlikowski
Proc. Amer. Math. Soc. 130(7) (2002), 2007-2013.
We show that the property
follows from the following two propositions:
- for every Darboux function g:R-->R there exists
a continuous nowhere constant function f:R-->R such that f+g is Darboux
which hold in the iterated perfect set model.
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 non-trivial interval
there exists a subset A of R of cardinality
continuum such that the restriction h|A of h to A
is uniformly continuous,
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Last modified March 30, 2002.