Abstract
In this paper we develop some combinatorial models for continuous spaces. 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 based on an obvious geometrical background. This work presents some discrete models ofn-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)-space-time. We are also discussing the question by R. Sorkin about how to derive the system of simplicial complexes from a system of open coverings of a topological space.
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Evako, A.V. Dimension on discrete spaces. Int J Theor Phys 33, 1553–1568 (1994). https://doi.org/10.1007/BF00670697
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DOI: https://doi.org/10.1007/BF00670697