Wu, Jingyi and Weatherall, James Owen (2023) Between a Stone and a Hausdorff Space. [Preprint]

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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 bifurcating curves.

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Item Type:	Preprint
Creators:	Creators Email ORCID Wu, Jingyi jingyi.wu@uci.edu 0000-0001-7198-851X Weatherall, James Owen weatherj@uci.edu 0000-0003-1461-7821
Keywords:	General Relativity, Einstein Algebras, Hausdorff Condition, Excess Structure
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories
Depositing User:	Jingyi Wu
Date Deposited:	06 May 2023 12:20
Last Modified:	06 May 2023 12:20
Item ID:	22076
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories
Date:	May 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/22076

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• Between a Stone and a Hausdorff Space. (deposited 06 May 2023 12:20) [Currently Displayed]
  • Between a Stone and a Hausdorff Space. (deposited 21 Oct 2023 01:32)

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