Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic values and Baire category


Author: Chaim Mida
Journal: Proc. Amer. Math. Soc. 41 (1973), 492-494
MSC: Primary 30A72
MathSciNet review: 0324046
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A72

Retrieve articles in all journals with MSC: 30A72


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0324046-0
PII: S 0002-9939(1973)0324046-0
Article copyright: © Copyright 1973 American Mathematical Society