eng Science and Education Publishing Applied Mathematics and Physics 2333-4886 2017-05-20 5 2 47 52 10.12691/amp-5-2-3 AMP2017523 article Alexander V. Evako evakoa@mail.ru 1 “Dianet”, Laboratory of Digital Technologies, Moscow, Russia 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≥3. 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. http://pubs.sciepub.com/amp/5/2/3/amp-5-2-3.pdf graph manifold discrete space non-spherical topology torus projective plane