The Order on the Light Cone and its induced Topology

Abstract

In this article we first correct a recent misconception about a topology that was suggested by Zeeman as a possible alternative to his Fine topology. This misconception appeared while trying to establish the causality in the ambient boundary-ambient space cosmological model. We then show that this topology is actually the intersection topology (in the sense of G.M. Reed) between the Euclidean topology on ${\mathbb{R}}^4$ and the order topology whose order, namely horismos, is defined on the light cone. Last, but not least, we show that the order topology from horismos belongs to the class of Zeeman topologies. These results accelerate the need for a deeper and more systematic study of the global topological properties of spacetime manifolds.

arXiv admin note: text overlap with arXiv:1706.07488

References in corpus (3)

• On the Orderability Problem and the Interval Topology
• Topology of the ambient boundary and the convergence of causal curves
• The causal order on the ambient boundary

Cited by in corpus (5)

• Spacetime Singularities vs. Topologies of Zeeman-Göbel Class
• Natural vs. Artificial Topologies on a Relativistic Spacetime
• On the Causal and Topological Structure of the $2$-Dimensional Minkowski Space
• Spacetimes as topological spaces, and the need to take methods of general topology more seriously
• Are four dimensions enough, a note on ambient cosmology