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

12/17/2017

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by   Alexander V. Evako, et al.

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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.