Between a Stone and a Hausdorff Space

Jingyi Wu; James Owen Weatherall

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arXiv · 2305.03871

Between a Stone and a Hausdorff Space

Jingyi Wu·James Owen Weatherall

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Abstract

We consider the duality between General Relativity and the theory of Einstein algebras, in the extended setting where one permits non-Hausdorff manifolds. We show that the duality breaks down, and then go on to discuss a sense in which general relativity, formulated using non-Hausdorff manifolds, exhibits excess structure when compared to Einstein algebras. We discuss how these results bear on a class of algebraically-motivated deflationist views about spacetime ontology. We conclude with a conjecture concerning non-Hausdorff spacetimes with no bifurcate curves.

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Jingyi Wu, James Owen Weatherall. 2023-05-05. Between a Stone and a Hausdorff Space. https://arxiv.org/abs/2305.03871

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