Dimension on Discrete Spaces

Details Dimension on Discrete Spaces Dimension on Discrete Spaces

1994-02-19

arxiv.org/abs/gr-qc/9402035v1

Int.J.Theor.Phys. 33 (1994) 1553-1568

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, 8 figures, Latex. Figures are not included, available from the author upon request. Preprint SU-GP-93/1-1. To appear

Scientific paper

10.1007/BF00670697

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.

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