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Continuous Boundary Behaviour for Functions Defined in the Open Unit Disc

Published online by Cambridge University Press:  22 January 2016

Leon Brown ,
P. M. Gauthier  and
Walter Hengartner
Leon Brown
Affiliation:
Wayne State University, Université de Montréal, Université Laval
P. M. Gauthier
Affiliation:
Wayne State University, Université de Montréal, Université Laval
Walter Hengartner
Affiliation:
Wayne State University, Université de Montréal, Université Laval
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This paper deals with cluster sets. While cluster sets can be considered in a more abstract setting, we shall limit ourselves to the study of functions f defined in the open unit disc D of the complex plane and taking their values on the Riemann sphere C̅. For p a point of the unit circle C, we denote by C(f,p) the cluster set of f at p, i.e., the set of all values w ∈ C̅ for which there is a sequence {zn}, zn ∈ D, such that zn → p and f(zn) → w. The point p is called a point of determination for f if C(f, p) is a singleton. In Section 1 we characterize the set of points of determination of a function f defined in D.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 57 , June 1975 , pp. 49 - 58
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

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