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  • Author or Editor: Krzysztof Ciesielski x
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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,y 3 ), is not density continuous [1]. 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.

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We prove that axiom CPAgame prism, 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.

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