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Proceedings of the American Mathematical Society

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Asymptotic values and Baire category

Author: Chaim Mida
Journal: Proc. Amer. Math. Soc. 41 (1973), 492-494
MSC: Primary 30A72
MathSciNet review: 0324046
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Abstract: Let $ f$ be meromorphic in the unit disc, and let $ \alpha $ be a complex number. Given $ \varepsilon > 0$, let $ {T_\varepsilon }(\alpha )$ denote the set of points $ {e^{i\theta }}$ for which the cluster set $ {C_\mathcal{L}}(f,{e^{i\theta }})$ lies in the $ \varepsilon $-neighbourhood of $ \alpha $ for some arc $ \mathcal{L} \to {e^{i\theta }}$. Then a sufficient condition that the set of points on the unit circle at which $ f$ possesses point-asymptotic value $ \alpha $ be of first category is that $ {T_\varepsilon }(\alpha )$ contains no arc for some $ \varepsilon > 0$.

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