Subject: Computer Science And Mathematics, Geometry And Topology Keywords: causality; chronology; chorology; Minkowski space; time cone; space cone; weak interval topology; duality
Online: 24 May 2019 (08:22:25 CEST)
We give an exact mathematical construction of a spacelike order $<$, which is dual to the standard chronological order $\ll$ in the $n$-dimensional Minkowski space $M^n$ and we discuss its order-theoretic, geometrical as well as its topological implications, conjecturing a possible extension to curved spacetimes.
ARTICLE | doi:10.20944/preprints201902.0097.v1
Subject: Computer Science And Mathematics, Geometry And Topology Keywords: sliced spaces; global hyperbolicity; product topology; Alexandrov topology
Online: 12 February 2019 (09:48:42 CET)
We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.