History
The practice of allowing function in mathematics to mean also multivalued function dropped out of usage at some point in the first half of the twentieth century. Some evolution can be seen in different editions of A Course of Pure Mathematics by G. H. Hardy, for example. It probably persisted longest in the theory of special functions, for its occasional convenience.
The theory of multivalued functions was fairly systematically developed for the first time in Claude Berge's Topological spaces (1963).
Read more about this topic: Multivalued Function
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