In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:R2?R2,G(x,y)=(x,y3), is not density continuous . We will also characterize those analytic functions which are strongly density continuous at the given pointa ? C. From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b ? C andb is either real or imaginary.
Authors:Krzysztof Ciesielski and Janusz Pawlikowski
We prove that axiom CPAgameprism, which follows from the Covering Property Axiom CPA and holds in the iterated perfect set model, implies that there exists
a Hamel basis which is a union of less than continuum many pairwise disjoint perfect sets. We will also give two consequences
of this last fact.