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Interpreting Non-Hausdorff (Generalized) Manifolds in General Relativity

Published online by Cambridge University Press:  01 January 2022

Joanna Luc  and
Tomasz Placek
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Abstract

The article investigates the relations between Hausdorff and non-Hausdorff manifolds as objects of general relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together some Hausdorff manifolds. In the light of this result, we investigate a modal interpretation of a non-Hausdorff differential manifold, according to which it represents a bundle of alternative space-times, all of which are compatible with a given initial data set.

Type
Articles
Information
Philosophy of Science , Volume 87 , Issue 1 , January 2020 , pp. 21 - 42
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

We gratefully acknowledge the support of the National Science Center for Joanna Luc (research grant Opus 2016/23/B/HS1/00464 ) and the support of the WSN2017 program of the Foundation for Polish Science for Tomasz Placek. For fruitful discussions we thank the audiences of meetings of the Southern California Philosophy of Physics Group, British Society for the Philosophy of Science Annual Conference in Oxford, and Modality in Physics conference in Kraków. We are also grateful to three anonymous referees of this journal for their helpful comments.

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