维万蒂关于多值解析函数值集的思想探析  

The Analysis of Vivanti's Thought on the Value Set of Multivalued Analytic Functions

作　　者：王全来[1] WANG Quanlai(The Department of Computer and Information Engineering,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学计算机与信息工程学院,天津300387

出　　处：《中国科技史杂志》2024年第3期423-434,460,共13页The Chinese Journal for the History of Science and Technology

基　　金：国家自然科学基金资助项目(项目编号:10771169);天津市教改项目(项目编号:B231006504);天津师范大学教改重点项目(项目编号:JGZD01218010)。

摘　　要：康托尔首先猜测多值函数的值集可能为可数集。维万蒂采用黎曼曲面思想首先发表了遭质疑的证明。依据原始文献,利用历史分析和比较的方法,指出:维万蒂涉及该问题的主动因是雅可比1835年的一篇文章;采用黎曼曲面的思想是受到了卡索拉蒂的影响;工作的理论基础是庞加莱的函数单值性定理。在此基础上,深入分析了维万蒂的思想认识过程及受到的质疑。他的工作对庞加莱、沃尔泰、拉佩雷斯-马可有重要影响,对其在集合论和函数奇点研究方面有一定激励作用。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.

关 键 词：多值函数 黎曼曲面 解析开拓 可数集 

分 类 号：N09[自然科学总论—科学技术哲学] O1[理学—数学]