A New Causal Topology and Why the Universe is Co-compact

Details A New Causal Topology and Why the Universe is Co-compact A New Causal Topology and Why the Universe is Co-compact

2011-12-05

arxiv.org/abs/1112.0817v2

Physics

Mathematical Physics

15 pages, AMS LaTeX. Some typos and language errors corrected, some comments and remarks shortened and slightly reformulated.

Scientific paper

We show that there exists a canonical topology, naturally connected with the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by quantum gravity. Taking a causal site compatible with Minkowski space, on every compact subset our topology became a reconstruction of the original topology of the spacetime (only from its causal structure). From the global point of view, the reconstructed topology is the de Groot dual or co-compact with respect to the original, Euclidean topology. The result indicates that the causality is the primary structure of the spacetime, carrying also its topological information.

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