TL;DR
This paper surveys the topologies of branching space-times, challenging the common belief that such structures must be non-Hausdorff, and clarifies the topological conditions for branching universes.
Contribution
It provides a comprehensive analysis of branching space-time topologies and refutes the misconception that they necessarily lack the Hausdorff property.
Findings
Branching space-times can have Hausdorff topologies.
The popular non-Hausdorff assumption is not universally required.
The paper clarifies conditions under which branching universes are Hausdorff.
Abstract
The purpose of this paper is to survey the possible topologies of branching space-times, and, in particular, to refute the popular notion in the literature that a branching space-time requires a non-Hausdorff topology.
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