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Home > Journals > SCIREA Journal of Mathematics > Archive > Paper Information

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

Volume 3, Issue 1, February 2018    |    PP. 29-56    |PDF (1033 K)|    Pub. Date: January 14, 2018
135 Downloads     1400 Views  

Author(s)
Alexander V. Evako, Npk Novotek, Moscow, Russia

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, we show that a digital (n-1)-sphere S in a digital simply connected n-manifold M is a separating space for M, and if a digital 3-manifold M is locally simply connected, then M is a digital 3-sphere.

Keywords
Digital Topology; Topological space; Separation; Digital simply connected space

Cite this paper
Alexander V. Evako, Properties of Digital n-Dimensional Spheres and Manifolds. Separation of Digital Manifolds, SCIREA Journal of Mathematics. Vol. 3 , No. 1 , 2018 , pp. 29 - 56 .

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