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

2011/12/05 by Martin Maria Kovár, Kovár, Martin Maria · 3 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #General Topology (math.GN) #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc #math-ph #math.GN #math.MP

paper · pdf · doi:10.48550/arxiv.1112.0817

15 pages, AMS LaTeX. Some additional typos corrected

openalex publication_date 2011/12/05 · arxiv created 2013/08/01 · arxiv updated 2013/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Causality Implies the Lorentz Group

Cited by

• Causal and Topological Aspects in Special and General Theory of Relativity
• Proximal groupoid patterns In digital images
• The Framework, Causal and Co-compact Structure of Space-time

Related

• The Framework, Causal and Co-compact Structure of Space-time
• On the Axioms of Causal Set Theory
• Topology Change in Classical General Relativity
• Non-Commutative Topology for Curved Quantum Causality
• Spacetime topology from causality