Ordinary and strong density continuity of complex analytic functions


Krzysztof Ciesielski

Period. Math. Hungar. 31 (1995), 11-20

In the paper it is proved that the complex analytic functions are (ordinarily) density continuous. This stay in contrast with the fact that even such a simple function as G:R2-->R, G(x,y)=(x,y3), is not density continuous. (See K. Ciesielski, W. Wilczynski, Density continuous transformations on R2, Real Anal. Exchange 20 (1994-95), 102-118.) We will also characterize those analytic functions which are strongly density continuous at the given point a in the complex plane C. From this we conclude that a complex analytic function f is strongly density continuous if and only if f(z)= a + b z, where a and b are in C and b is either real or imaginary.

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Last modified April 24, 1999.