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May 2010 A Lindelöf Property for Uniformly Normal Families
Richard E. Bayne, Myung H. Kwack
Missouri J. Math. Sci. 22(2): 130-138 (May 2010). DOI: 10.35834/mjms/1312233143

Abstract

In this note we present a simple new proof for a Lindelöf property for a normal map accessible to advanced undergraduate students. The proof extends the result to uniformly normal families: If $\{ f_n :D \to P^1(\mathbb{C})\}$ is a uniformly normal sequence from the unit disk $D$ in the complex plane ${\bf \mathbb{C}}$ into the Riemann Sphere $P^1(\mathbb{C})$ such that $\lim _{r_n \to 1}f_n(r_n)$ exists for all $ \{r_n\}\subset (0,1),$ then the sequence $\{f_n\}$ has non-tangential limit at $1$.

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Richard E. Bayne. Myung H. Kwack. "A Lindelöf Property for Uniformly Normal Families." Missouri J. Math. Sci. 22 (2) 130 - 138, May 2010. https://doi.org/10.35834/mjms/1312233143

Information

Published: May 2010
First available in Project Euclid: 1 August 2011

zbMATH: 1208.30033
MathSciNet: MR2675408
Digital Object Identifier: 10.35834/mjms/1312233143

Subjects:
Primary: 32A10‎
Secondary: 32A18 , 32A19

Rights: Copyright © 2010 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.22 • No. 2 • May 2010
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