  In this paper we develop some combinatorial models for continuous spaces. In
this spirit we study the approximations of continuous spaces by graphs,
molecular spaces and coordinate matrices. We define the dimension on a discrete
space by means of axioms, and the axioms are based on an obvious geometrical
background. This work presents some discrete models of n-dimensional Euclidean
spaces, n-dimensional spheres, a torus and a projective plane. It explains how
to construct new discrete spaces and describes in this connection several
three-dimensional closed surfaces with some topological singularities
  It also analyzes the topology of (3+1)-spacetime. We are also discussing the
question by R. Sorkin [19] about how to derive the system of simplicial
complexes from a system of open covering of a topological space S.
