Normal Family - Naming

Naming

Paul Montel coined the term "normal family" in 1912.

Note that this is a classical definition that, while very often used, is not really consistent with modern naming. In more modern language, one would give a metric on the space of continuous (holomorphic) functions that corresponds to convergence on compact subsets and then you would say "precompact set of functions" in such a metric space instead of saying "normal family of continuous (holomorphic) functions". This added generality however makes it more cumbersome to use since one would need to define the metric mentioned above.

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