数字流形与Jordan-Brouwer定理
Digital Manifolds and the Theorem of Jordan-Brouwer
摘要：
本文回答了T. Y. Kong在他的文章“Can 3-D Digital Topology be Based on Axiomatically Defined Digital Spaces？在这篇文章中，他问的问题，如果所谓的“好对”的邻里关系可以找到对集Z^n，使存在的数字流形的维数n-1，分离其补充在两个连接的集，是保证。为了实现这一点，我们使用了M.在Z^n中给出的一个集合被转化为一个单纯复形，它可以用来研究原始离散点集的拓扑性质。通过这种方式，人们能够定义（n-1）维数字流形的概念，并证明乔丹-布劳威尔定理的数字模拟。
英文摘要：
We give an answer to the question given by T.Y.Kong in his article "Can 3-D Digital Topology be Based on Axiomatically Defined Digital Spaces?" In this article he asks the question, if so called "good pairs" of neighborhood relations can be found on the set Z^n such that the existence of digital manifolds of dimension n-1, that separate their complement in exactly two connected sets, is guaranteed. To achieve this, we use a technique developed by M. Khachan et.al. A set given in Z^n is translated into a simplicial complex that can be used to study the topological properties of the original discrete point-set. In this way, one is able to define the notion of a (n-1)-dimensional digital manifold and prove the digital analog of the Jordan-Brouwer-Theorem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
