罗伯特·李·穆尔对点集拓扑学的贡献及影响

Robert Lee Moore s contributions and influence on point set topology

点集拓扑学是起源于17—19世纪、兴起于20世纪的重要数学分支.20世纪20、30年代是点集拓扑学的形成和发展时期,美国数学家罗伯特·李·穆尔在这一时期十分活跃,在点集理论、连续统理论、连续曲线和位置性质领域做出一系列突出贡献.本文立足于原始文献,详细考证了穆尔在点集拓扑学的工作,包括点集理论、连续统结构、曲线理论和位置性质等方面,明确了穆尔在拓扑学上产生的一系列影响,包括穆尔空间、球面和流形、上半连续分解理论等方面.

Point set topology is an important branch of mathematics which originated from 17th to 19th century and emerged in 20th century.The 1920s and 1930s were the formative and developing period of point set topology.Robert Lee Moore,an American mathematician,was very active during this period and made a series of outstanding contributions in the field of point set theory,continuum theory,continuous curves and position properties.Based on the original literature,this paper reviews Moore s work of point set topology in detail,including point set theory,continuum structure,curve theory and position properties,and makes clear a series of Moore s influence on topology,including Moore space,spherical and manifold,upper semi-continuous decomposition theory and so on.