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Computational Methods and Function Theory 8 (2008), No. 1, 195--198
Copyright Heldermann Verlag 2008

A Montel Theorem for Holomorphic Functions on Infinite Dimensional Spaces that Omit the Values 0 and 1

Clifford J. Earle
cliff@math.cornell.edu , Cornell University, Department of Mathematics, Ithaca, NY 14853--4201, U.S.A.

[Abstract-pdf] [Abstract-ps]

Let X be a connected complex Banach manifold. We give a proof that the set of holomorphic functions on X that omit the values 0 and 1 is a normal family.

Keywords: Montel's Theorem, normal families.

MSC 2000: 46G20.

[FullText-pdf (190 K)] [FullText-ps (323 K)]