Mathematical Sciences: Some Problems in Boundedly ControlledTopology

安德森教授打算研究有界控制拓扑及其应用领域中的几个问题。这项工作将建立在他与丹麦欧登塞大学的汉斯·约尔根·蒙克霍尔姆教授共同开发的这一学科的基础上。这些问题有三种类型：有些问题只存在于有界控制拓扑的范围内，旨在进一步发展该学科的基础；有些问题旨在更准确地探索有界控制拓扑和由T.A.Chapman教授和F.S.Quinn III教授独立发展的epsilon控制拓扑之间的关系；还有一些涉及到将有界控制拓扑学的方法和结果应用到其他领域，例如研究群体行动。

Professor Anderson intends to work on several problems in the area of boundedly controlled topology and its applications. This work will build on the foundations of this subject that he has developed in joint work with Professor Hans Jorgen Munkholm of Odense University, Denmark. The problems are of three types: Some lie solely within the confines of boundedly controlled topology and are intended to develop further the foundations of that subject; some are designed to explore more exactly the relationship between boundedly controlled topology and the epsilon-controlled topology developed independently by Professors T. A. Chapman and F. S. Quinn III; and some involve applying the methods and results of boundedly controlled topology to other areas, for example to the study of group actions.