Mathematical Sciences: Upstate New York Topology Seminar

道格拉斯河安德森将致力于几个问题， 有界控制拓扑及其应用领域。 有些问题是为了扩大 方法的有界控制拓扑结构，通过将它们应用到 其他领域的问题，而其他领域的问题则完全在 有界控制拓扑的域本身。 试图 扩大方法的范围旨在证明其 相关性，并澄清其局限性，并可能暴露额外的 这是需要解决的问题。 的 该领域内的问题本身代表了研究的延伸 安德森和H.来自丹麦欧登塞的J. Munkholm。 目的是更清楚地了解 拓扑的这一部分与 受控拓扑结构是由T. A. S.查普曼C. Ferry和F. S.奎因，如果有必要， 在一定范围内扩充基础结果的主体 受控拓扑 拓扑学是研究几何对象的性质的学科 它们不会被连续的变换所破坏， 像连通性、打结性等等。 拓扑性质是基本的和普遍存在的， 长度和面积的几何性质，但他们称之为 完全不同的技术来处理它们。 这时 高维度的拓扑结构已经被密集地开发，并且 可用的技术种类相当广泛。 从时间 在一个主题的发展过程中，有必要 组织其方法，使其更容易用于 更容易传递给后代， 我希望使用它们，而不是直接参与他们的工作。 发明的 这样的时间出现在高维拓扑中， 有界控制的方法是一种自然的编码方法， 这一原则被证明在工具箱中的秩序中是有用的， 可以这么说。

Douglas R. Anderson will work on several problems in the areas of boundedly controlled topology and its applications. Some of the problems are designed to expand the uses of the methods of boundedly controlled topology by applying them to problems in other areas, while others lie entirely within the domain of boundedly controlled topology itself. Attempts to expand the scope of the methods are intended to demonstrate their relevance and clarify their limitations and may expose additional questions within the subject which need to be addressed. The problems within the area itself represent extensions of research already done by Anderson and H. J. Munkholm of Odense, Denmark. The objectives are to understand more clearly the exact relationship between this part of topology and the versions of controlled topology introduced by such other researchers as T. A. Chapman, S. C. Ferry, and F. S. Quinn, and, if necessary, to enlarge the body of foundational results within boundedly controlled topology. Topology is the study of properties of geometric objects which are not destroyed by continuous transformations, such properties as connectedness, knottedness, and so forth. Topological properties are as basic and ubiquitous as the more familiar geometric properties of length and area, but they call for entirely different techniques to deal with them. By now the topology of high dimensions has been intensively developed, and the array of techniques available is quite extensive. From time to time in the development of a subject, it becomes necessary to organize its methods to make them more readily available to others and easier to pass on to future generations which will wish to use them without having been directly involved in their invention. Such a time has arisen in high dimensional topology, and the boundedly controlled approach is a natural codifying principle that is proving useful in making order in the toolbox, so to speak.