Properties of Digital n-Dimensional Spheres and Manifolds. Separation of Digital Manifolds

TL;DR

This paper explores fundamental properties of digital n-dimensional manifolds and spheres, including separation properties, structural features, and methods for simplifying digital manifolds through contractions.

Contribution

It establishes key properties of digital n-manifolds and spheres, including their separation characteristics and a method for compressing digital manifolds via point contractions.

Findings

Digital n-sphere M satisfies M-v is a digital n-disk for any point v.

A digital (n-1)-sphere in a digital n-manifold acts as a separating space.

Digital n-manifolds can be simplified through sequential contractions.

Abstract

In the present paper, we study basic properties of digital n-dimensional manifolds and digital simply connected spaces. An important property of a digital n-manifold is that M is a digital n-sphere if and only if for any point v of M, M-v is a digital n-disk. It is proved that a digital (n-1)-sphere S contained a digital n-sphere M is a separating space of M. We show that a digital n-manifold can be converted to the compressed form by sequential contractions of simple pairs of adjacent points. We study structural features of digital simply connected spaces. In particular, a digital (n-1)-sphere S in a digital simply connected n-manifold M is a separating space of M.