English

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

Mathematical Physics 2013-08-05 v3 General Relativity and Quantum Cosmology General Topology math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.1112.0817,
  title  = {A New Causal Topology and Why the Universe is Co-compact},
  author = {Martin Maria Kovár},
  journal= {arXiv preprint arXiv:1112.0817},
  year   = {2013}
}

Comments

15 pages, AMS LaTeX. Some additional typos corrected