仿拓扑群中的三空间问题

项目名称： 仿拓扑群中的三空间问题

项目编号： No.11471153

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 林寿

作者单位： 闽南师范大学

项目金额： 60万元

中文摘要： 拓扑与代数的结合由来已久。由一般拓扑学与抽象代数学融合而发展起来的拓扑代数已渐成活跃的前沿研究领域之一。近年来本项目组成员开辟了拓扑代数中广义度量空间理论的研究途径。本项目将围绕2008年出版的《Topological Groups and Related Structures》等中关于（仿）拓扑群的三空间的若干问题，借助集合论、拓扑学、代数学与统计学中的成功方法，寻求 Arhangelskiǐ及Tkachenko问题的解决，逐步形成国内拓扑代数的研究基地，在有国际影响的刊物上发表论文30篇以上，出版著作1部，使我们的若干研究工作能处于国际前沿。

中文关键词： 拓扑群；仿拓扑群；广义度量空间；三空间性质；映射

英文摘要： The combination of topology and algebra has a long-standing history. From the intersection and integration of topology and algebra, there generates the theory of the topological algebra, which has become one of the active front research field in the study of general topology. In recent years, members of the project team have opened up the research approach to the theory of generalized metric spaces in Topology Algebra. Focusing on several open problems about three spaces in (para-)topological groups raised in the 2008 edition of monograph Topological Groups and Related Structures, the project team will explore approaches of solving Arhangelsk'iǐ and Tkachenko's problems by using methods of set theory, topology, algebra and statistics, and will form gradually a research base of Topological Algebras in China. The project team goals at to publish more than 30 papers in journals with international influence and one monograph, and to make our research work being on the frontier of the field.

英文关键词： topological groups;paratopological groups;generalized metric spaces;three space properties;mappings