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A Note on Extended Ambiguous Points

Published online by Cambridge University Press:  22 January 2016

J.L. Stebbins
J.L. Stebbins*
Affiliation:
University of Wisconsin-Milwaukee
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Let f be an arbitrary function from the open unit disk D of the complex plane into the Riemann sphere S. If p is any point on the unit circle C, C(f, p) is the set of all points w such that there exists in D a sequence of points {Zj} such that zj→p and f(zj)→w. CΔ(f, p) is defined in the same way, but the sequence {Zj} is restricted to Δ⊂D. If α and β are two arcs in D terminating at p and Cα(f, p)∩Cβ(f, p) = Φ, p is called an ambiguous point for f.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 43 , September 1971 , pp. 167 - 168
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Bagemihl, F., Curvilinear cluster sets of arbitrary functions. Proc. Nat. Acad. Sci. U.S.A. 41, 379–382 (1955).Google Scholar
[2] Gross, W., Zum Verhalten analytischer Funktionen in der Umgebung singulãrer Stellen. Math. Z. 2, 243–294 (1918).Google Scholar
[3] Mathews, H.T., A note on Bagemihl’s ambiguous point theorem. Math. Z. 90, 138–139 (1965).CrossRefGoogle Scholar