维托尔德·胡列维茨与20世纪的拓扑学

Witold Hurewicz and Topology in the 20^(th) Century

波兰裔数学家胡列维茨是同伦群理论的创始人,维数论的开创者之一,他在描述集合论中亦有出色的研究。从20世纪20年代开始,胡列维茨先后在维也纳大学、阿姆斯特丹大学这两个欧洲当时的拓扑学中心学习和研究,之后还差点来到北京大学数学系任教。二战后,移居美国的胡列维茨在正合序列、纤维空间上的工作又推动了代数拓扑学的发展。在麻省理工学院的辐射实验室,胡列维茨的应用数学才华在雷达的研制过程中发挥了作用。本文对胡列维茨的学术经历进行补全与深入挖掘,旨在更好地理解拓扑学发展历程中的若干关键节点。

Polish-born mathematician Hurewicz is the founder of modern Homotopy theory and one of the pioneers of Dimension theory, and made outstanding research in Descriptive Set theory. From the 1920 s, Hurewicz studied and did research at two European topology centers: University of Vienna and University of Amsterdam,and he almost came to China to teach at the Department of Mathematics of Peking University later. After World War II, Hurewicz made great progress in exact sequence and fibre space which promoted the development of algebraic topology again. At the Radiation Laboratory of the Massachusetts Institute of Technology, Hurewicz’s talent for applied mathematics helped the research of radar. This paper complements and deeply explores the academic experience of Hurewicz in order to better understand the key points in the evolution of topology.