Digital n-Pseudomanifold and n-Weakmanifold in a Binary (n + 1)-Digital Image

Abstract

We introduce the notion of digital n-pseudomanifold and digital n-weakmanifold in (n+1)-digital image, in the context of (2n, 3 n −1)adjacency, and prove the digital version of the Jordan-Brouwer separation theorem for those classes. To accomplish this objective, we construct a polyhedral representation of the n-digital image, based on cubical complex decomposition. This enables us to translate some results from polyhedral topology into the digital space. Our main result extends the class of "thin" objects that are defined locally and verifies the Jordan-Brouwer separation theorem.