Periodica Mathematica Hungarica

, Volume 31, Issue 1, pp 11–20 | Cite as

Ordinary and strong density continuity of complex analytic functions

  • Krzysztof Ciesielski
Article
  • 13 Downloads

Abstract

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 [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.

Mathematics subject classification numbers, 1991

Primary 26B05 26A15 Secondary 30A99 

Key words and phrases

Strong density continuity complex analytic functions 

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References

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Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • Krzysztof Ciesielski
    • 1
  1. 1.Department of MathematicsWest Virginia UniversityMorgantownUSA

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