Properties of Digital n-Dimensional Spheres and Manifolds. Separation of Digital Manifolds
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Author(s)
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.
Volume 3, Issue 1, February 2018 | PP. 29-56.
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