This paper presents discretization schemes for building graph theoretical models of n-dimensional continuous objects with the same topological properties as their continuous counterparts. An LCL collection of n-cells in Euclidean space is introduced and investigated. The digital model of a continuous n-dimensional object is the intersection graph of an LCL cover of the object. We prove that the digital model of a continuous closed n-dimensional manifold is a digital closed n-dimensional manifold. It is shown that the digital model of a continuous n-dimensional sphere is a digital n-sphere with at least 2n+2 points, the digital model of a continuous projective plane is a digital projective plane with at least eleven points and the digital model of a continuous Klein bottle is the digital Klein bottle with at least sixteen points.

graph, manifold, digital space, sphere, Klein bottle, projective plane, Moebius band