@article{amp2017523,
author={Evako, Alexander V.},
title={Graph Theoretical Models of Discrete Spaces with Locally Non-spherical Topology},
journal={Applied Mathematics and Physics},
volume={5},
number={2},
pages={47--52},
year={2017},
url={http://pubs.sciepub.com/amp/5/2/3},
issn={2333-4886},
abstract={A graph theoretical model of a continuous space is a graph with the same topological structure as its continuous counterpart. A digital closed n-dimensional manifold with a locally spherical topology is a graph theoretic model for a continuous closed n-dimensional manifold. This paper defines and studies properties of a new class of digital n-dimensional spaces with a locally non-spherical topology. We prove that such spaces have the dimension n¡Ý3. We define and investigate properties of digital 3- and 5-dimensional closed surfaces with a local toroidal and projective plane topology. These spaces have no direct continuous counterparts among n-dimensional manifolds in classical topology. These results arise questions like what physical, chemical or biological structures can be described by digital n-dimensional surfaces with a locally non-spherical topology.},
doi={10.12691/amp-5-2-3}
publisher={Science and Education Publishing}
}