On the Causal and Topological Structure of the $2$-Dimensional Minkowski Space

Abstract

A list of all possible causal relations in the $2$-dimensional Minkowski space $M$ is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating the causal structure of $M$. Generalisations of these results are discussed, as well as their significance in a discussion on spacetime singularities.