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A Note on Extended Ambiguous Points

Published online by Cambridge University Press:  22 January 2016

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
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

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[3] Mathews, H.T., A note on Bagemihl’s ambiguous point theorem. Math. Z. 90, 138139 (1965).CrossRefGoogle Scholar