Digital Manifolds and the Theorem of Jordan-Brouwer
Authors: Martin Hünniger
Summary: We give a solution to the query given by T.Y.Kong in his article “Can 3-D Digital Topology be Primarily based on Axiomatically Outlined Digital Areas?” On this article he asks the query, in that case known as “good pairs” of neighborhood relations might be discovered on the set Z^n such that the existence of digital manifolds of dimension n-1, that separate their complement in precisely two linked units, is assured. To realize this, we use a way developed by M. Khachan et.al. A set given in Z^n is translated right into a simplicial advanced that can be utilized to check the topological properties of the unique discrete point-set. On this method, one is ready to outline the notion of a (n-1)-dimensional digital manifold and show the digital analog of the Jordan-Brouwer-Theorem