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A Montel theorem for holomorphic functions on infinite dimensional spaces that omit the values 0 and 1. (English) Zbl 1172.46030
Consider the family of holomorphic maps from a connected complex Banach manifold into the Riemann sphere, omitting three specified values. The author proves that this family is normal in the sense that every net contains a subnet converging in the compact-open topology to either a member of the family or one of the three constant maps determined by the omitted values.

MSC:
46G20 Infinite-dimensional holomorphy
32A19 Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.)
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References:
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