The Analysis of Vivanti's Thought on the Value Set of Multivalued Analytic Functions
G.Cantor first guessed that the value set of multivalued functions may be countable.G.Vivanti first published an imperfect proof by the idea of Riemannian surfaces.Based on the original literature,the article points out that the active cause of Vivanti's involvement in this problem is an article of J.Jacobi in 1835 by historical analysis and comparison methods;the idea of using Riemannian surfaces was influenced by F.Casorati;the theoretical basis of the work is Poincaré's theorem on the uniformization of the functions.On the basis of these content,this paper analysizes the process of Vivanti's ideological understanding and the doubts which he had received.It studies his significant influence on H.Poincaré,V.Volterra and R.Pérez-Marco.Vivanti's work has a certain impact on his own research in set theory and function singularities.
multivalued functionsRiemann surfaceanalytic continuationcountable set
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