# On the Possibility of Singularities on the Ambient Boundary

## TL;DR

This paper examines the role of different topologies in spacetime models, questioning previous claims that certain topologies prevent singularity formation, and suggests directions for refining cosmological models.

## Contribution

It critically reviews the use of Zeeman topologies in ambient boundary models and proposes new questions to improve understanding of spacetime singularities.

## Key findings

- Zeeman $Z$ topology is coarser than the Fine Zeeman Topology $F$
- Causal curves under $Z$ are piecewise null
- Questions the previous conclusion that $Z$ prevents singularities

## Abstract

The order horismos induces the Zeeman $Z$ topology, which is coarser than the Fine Zeeman Topology $F$. The causal curves in a spacetime under $Z$ are piecewise null. $F$ is considered to be the most physical topology in a spacetime manifold $M$, as the group of homeomorphisms of $M$ is isomorphic to the group of homothetic transformations of $M$. $Z$ was used in the Ambient Boundary-Ambient Space cosmological model, in order to show that there is no possibility of formation of spacetime singularities. In this article we question this result, by reviewing the corresponding articles, and we propose new questions towards the improvement of this model.